SSC CDS
BANKrAILWAY
ª Concepts with Visual Understanding
ª Core Physics (Detailed Theory)
Physics
ª Practical Applications of Physics
ª Previous year Questions from
1999 to till date
C L A S S E S
Chapter - 17
(Thermal Properties of Matter)
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THERMAL PROPERTIES OF MATTER Heat
Heat is a form of energy, which produces the sensation of warmth. It is responsible for the change in thermal condition of the body.
Its SI unit is 'joule' and cgs unit is ' calorie' which is also, widely used. When a body gets heated, various types of change occurs such
as expansion, contraction, change of state, change of electrical properties, etc. The heat energy that is transferred from one body to
another, can change into mechanical energy, electrical energy, etc.
Temperature
Temperature is a quantity, that expresses the degree of hotness or coldness of a body. The flow of heat from one body to another
body is due to their temperature difference, e.g., if on dropping a very hot spoon in water container, containing cool water, heat
flows from spoon to the water. So, it is clear that temperature and heat are different things. It is measured in several arbitrary
scale: like Celcius, Fahrenheit, Kelvin, Reaumur.
Measurement of Temperature
The device which measures the temperature of the body is called thermometer. It was developed by Galileo, who found that the
gases expand on heating. As temperature is a variable quantity in different conditions. Therefore, different scales are provided to
measure it.
Temperature Scales
To measure temperature, two fixed points are taken. One of them is the freezing point of water, known as ice point and other fixed
point is boiling point of water, known as steam point.
Some temperature scales are as follows
Celsius Scale (°C)
In this scale, temperature is fixed from 0 (zero). Scale is divided into 100 equal parts called degrees. Ice point and steam point are
taken as 0°C and 100°C. This scale was designed by Anders Celsius in 1710.
Fahrenheit Scale (°F)
In this scale, ice point and steam point are taken as 32° F and 212° F respectively. This scale is divided into 180 equal parts. It was
designed by Gabriel Fahrenheit in 1717.
Kelvin Scale (K)
In this scale, ice point and steam point are taken as 273 K and 373 K, respectively. This scale is divided into 100 equal parts. It was
introduced by Kelvin in 1724.
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Reaumur Scale (R)
In this scale, ice point and steam point are taken as 0 R and 80 R. This scale was introduced by RA Reaumur in 1730.
Rankine Scale (Ra)
In this scale, ice point and steam point are taken as 460 Ra and 672 Ra. It was introduced by JM Ranking in 1859.
Relations between various temperature scales are as follow
C F 32 R K 273 Ra 460
100 180 80 100 212
Transmission of Heat
Transfer of heat from one place to other place is called transmission of heat. There are three processes by which transmission of
heat takes place.
1. Conduction
It is the process of transmission of heat, in which heat goes from one particle to another
particle of substance but no particle leaves its position. In solids, transmission of heat takes
place by conduction process.
In metals, thermal conduction is due to vibration of atoms and free electrons.
2. Convection
It is the process of transmission of heat, in which particles of substance goes to
another place after taking heat from the source and other particles come to their
place. In liquids and gases, transmission of heat takes place by convection process.
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Principle of chimney used in the kitchen or a factory is based on convection land and sea
breezes are due to the convection.
3. Radiation
It is the process of transmission of heat, in which there is no need of medium for
transfer of heat. It is the quickest way of transmission of heat. Heat from the sun comes
to the earth by radiation. Dark colored objects absorb radiation better than the light-
colored object.
Transformation of Phase
When matter changes from one state to another it is called a phase transition.
Various processes involved in this are:
• Gas to solid phase transitions are known as "deposition."
• Gas to liquid phase transitions are known as "condensation."
• Liquid to gas phase transitions are known as "vaporization."
• Liquid to solid phase transitions are known as "freezing."
• Solid to liquid phase transitions are known as "melting."
• Solid to gas phase transitions are known as "sublimation."
• Gas to plasma phase transition is known as Ionization
• Plasma to gasphase transition is known as Recombination.
Dry Ice - Solid carbon dioxide is known as "dry ice" and sublimates at room temperature.
Plasma is the fourth state of matter which does not have a fixed shape or volume and are less
dense than solids and liquids but unlike ordinary gases, they are made up of atoms in which few or
all the electrons have been stripped out and the ions move freely.
Triple point:
The triple point of a substance is the temperature and pressure at which the three phases of that substance(Solid, liquid and gas)
exist together in thermodynamic equilibrium.
Or It is that temperature and pressure at which the sublimation curve, fusion curve and the vaporization curve meet.
Triple point of water is 0.01 C
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There are many combinations of Pressure and Temperature where substancecoexist as (solid – liquid), or (liquid – gas) or (gas –
solid) phases.But there is only one combination of pressure and temperature at which the three phases can coexist as (solid, liquid
and gas phase), i.e.AT TRIPLE POINT
But there is a particular pressure and temperature combination or particular point in which increasing either pressure or
temperature or both, the substance cannot be distinguished whether it is a liquid or gas.The phase is called super critical fluid. This
point is called critical point of that substance.
s-v line where both solid and liquid form exists together
s-l line where both solid and vapour form exists together
l-v line where both liquid and vapour form exists together
Variation of melting & Boiling points with Temperature
Melting pointand boiling point varies with Temperature
Since our surroundings has Pressure= 1 atm. So, we consider value of Temperatureat 1 atm
boiling point = 100°C at 1 atm
Melting point= 0°C at 1 atm
Specific Heat
The amount of heat required to raise the temperature of 1 g of a substance by 1°C is called the specific heat of gas.
It is represented by s. Its unit is cal/g°C or joule/g°C.
s = Q
m t
where,
Q = amount of heat given to the substance
m = mass of the substance
Δt = rise in temperature
There are two types of specific heat of gases
1. Specific Heat at constant volume (cv)
At constant volume, the amount of heat required to raise the temperature of 1 g of a gas by 1°C is called specific heat at constant
volume (CV). Its unit is cal/g°C.
2. Specific Heat at Constant Pressure (cp)
At constant pressure, the amount of heat required to raise the temperature of 1 g of a gas by 1°C is called specific heat at constant
pressure (CP). Its unit is cal/g°C.
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Latent Heat
At constant temperature, the amount of heat taken by 1 g of a substance to change its state is called latent heat of substance. It is
represented by L, its unit is cal/g.
Latent heat of vaporization is inversely proportional to the temperature and is maximum at 0°C. Variation of latent heat of water
vapor with temperature is negative.
heat, Q = m(mass)× L(Specific latent heat) it happens at constant temperature
100
Ice Water
& Ice
Water all
liquid
Water
and Steam
(Steam)
Water
Vapour Mct
Latent Heat
0° C
Mct
Mct
Latent Heat
0
–20
–40°C 0 20 100 200 740
Heat added (k cal)
Calorific Value:
The amount of heat obtained by 1 g of a fuel is known as its calorific value. Out of all the substances, hydrogen has maximum
calorific value.
Note:If a pendulum designed at certain temperature is allowed to move/work at different temp. Then time difference is observed or
correct time is not shown.
Time is lost or gained by pendulum per second.
Calorimetry
It is the science of measuring the changes in the state variables of a body due to transfer of
heat in order to calculate the effect of heat transfer on obtained changes. This is performed
using Calorimeter.
Principle of Calorimeter
When two bodies of different temperature are kept in contact, then flow of heat between
them takes place from the body at higher temperature to the body at lower temperature. This
flow continues till both the bodies attain the same temperature.
Car Engine Coolant
Water is used as a cooling liquid in car engine because its specific heat capacity is high and
water absorbs more heat for each degree rise of its temperature. However, water alone is not
sufficient for cooling a car engine. One needs to add a coolant such as ethylene glycol,
potassium dichromate, tri-sodium phosphate, and sodium nitrate.
Entropy
It is the degree of order or randomness in thesystem and is thermodynamic function which depends only on the temperature of
system only.
Entropy (𝛿S) = Heat absorbed( Q)
Absolutetemperature(T)
𝛿Q = T𝛿S
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Entropy of a substance is zero at absolute zero temperature. Water at 0°C is assumed to have zero entropy, and changes in its
entropy are reckoned from this temperature.
Cooling at the night
The earth and other objects on it, receive solar radiation during the day and become
warm. But at night they start emitting radiant energy and become cool. Cloudy nights are
warmer than clear nights, because clouds reflect the radiations emitted by the earth at
night and keep it warm. Thus, clouds acts like a blanket.
Greenhouse effect
The radiation from the sun when reaches to the earth surface is of shorter wavelength,
some part of it is absorbed by the earth surface and some part is reflected back. The
reflected radiation is of larger wavelength So, it is trapped by the layer CO2 molecules
present in the atmosphere.So, the trapped radiations are reflected back towards the earth surface, thereby rising the temperature
of entire earth. This effect is known as Green house effect and the CO2 is known as Green house gas.
Newton's law of cooling
If a body is at higher temperature then surrounding than it looses heat to the surroundings
The rate of cooling of a body is directly proportional to the temperature difference of body and its surroundings.
e.g. hot water takes much less time in cooling from 100°C to 95°C than from 20°C to 15°C. If hot water and fresh tap water are kept
in a refrigerator, the rate of cooling of hot water will be faster than the tap water.
Mathematically, – 0
dQ(T T )
dt ⇒ Rate of heat loss, 0
dQk(T T )
dt
⇒
dms
dt
= k ( – surroundings)
Black body
A perfectly black body is one, which absorbs completely all the radiations of whatever wavelength is incident upon it. Since, it
neither reflect nor transmit any radiation, it appears black whatever the colour of the incident radiation may be.
Emissive Power (e)
It is defined as the amount of heat radiated by unit area of the surface in one second at a given temperature and for given
wavelengths. Its unit is J/m2 second.
Absorptive Power (a)
It is defined as the ratio of absorbed radiation to the total incident radiation. It has no unit.
The silvered surface of a thermo flask is a bad absorber. It does not absorb much heat from the surroundings. That is why ice inside the
flask does not melt. Also, the silver surface is a bad emitter/radiator, therefore hot liquids inside the flask do not cool quickly.
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KINETIC THEORY OF GASES The kinetic theory of gases describes a gas as a large number ofsubmicroscopic particles (atoms or molecules), all of which are in
constant, rapid, random motion. The randomness arises from the particles' many collisions with each other and with the walls of
the container.
Kinetic theory of gases explains the macroscopic properties of gases, such as pressure, temperature, viscosity, thermal
conductivity, and volume, by considering their molecular composition and motion. The theory posits that gas pressure results from
particles' collisions with the walls of a container at different velocities.
Assumptions of kinetic theory of gases
1. Every gas of extremely small particles known as molecules. The molecules of a given gas are all identical but are different from
those of another gas.
2. The molecules of a gas are identical spherical, rigid and perfectly elastic point masses.
3. The molecular size is negligible in comparison to intermolecular distance (10-9 m).
4. The speed of gas molecules lies between zero and infinity very high speed.
5. The distance covered by the molecules between two successive collisions is known as free path and mean of all free paths is known
as mean free path.
6. The number of collision per unit volume in a gas remains constant.
7. No attractive or repulsive force acts between gas molecules.
8. Gravitational forces on the molecules is ineffective due to small masses and very high speed of molecules.
Kinetic Theory of Matter
(a) Solids:It is the type of matter which has got fixed shape and volume. The force of attraction between any two molecules of a solid is
very large.
(b) Liquids:It is the type of matter which has got fixed volume but no fixed shape. Force of attraction between any two molecules is not
that large as in case of solids.
(c) Gases:It is the type of matter does not have any fixed shape or any fixed volume.
• Ideal Gas:A ideal gas is one which has a zero size of molecule and zero force of interaction between its molecules.
• Ideal Gas Equation:A relation between the pressure, volume and temperature of an ideal gas is called ideal gas equation.
PV/T = Constant or PV = nRT
Here, n is the number of moles and R is the universal gas constant
Real Gas:The gases which show deviation from the ideal gas behavior are called real gas.
• Vander wall’s equation of state for a real gas:
[P+(na/V)2][V-nb] = nRT
Here n is the number of moles of gas.
a and b are van der waals’ constants.
Avogadro’s number (N):Avogadro’s number (N), is the number of carbon atoms contained in 12 gram of carbon-12.
N = 6.023×1023
(a)To calculate the mass of an atom/molecule:
Mass of one atom = atomic weight (in gram)/N
Mass of one molecule = molecular weight (in gram)/N
(b)To calculate the number of atoms/molecules in a certain amount of substance:
Number of atoms in m gram = (N/atomic weight)×m
Number of molecules in m gram = (N/molecular weight)×m
(c)Size of an atom:
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Volume of the atom, V = (4/3)πr3
Mass of the atom, m = A/N
Here, A is the atomic weight and N is the Avogadro’s number.
Radius, r =[3A/4πNρ]1/3
Here ρ is the density.
Gas laws
(a) Boyle’s law:It states that the volume of a given amount of gas varies inversely as its pressure, provided its temperature is kept
constant.
PV = Constant
(b) Charler's law or GayLussac’s law:It states that volume of a given mass of a gas varies directly as its absolute temperature,
provided its pressure is kept constant.
V/T= Constant
V–V0/V0t = 1/273 = γp
Here γp (=1/273) is called volume coefficient of gas at constant pressure.
Volume coefficient of a gas, at constant pressure, is defined as the change in volume per unit volume per degree centigrade rise of
temperature.
(c) Gay Lussac’s law of pressure: It states that pressure of a given mass of a gas varies directly as its absolute temperature provided
the volume of the gas is kept constant.
P/T = P0/T0 or P – P0/P0t = 1/273 = γp
Here γp (=1/273) is called pressure coefficient of the gas at constant volume.
Pressure coefficient of a gas, at constant volume, is defined as the change in pressure per unit pressure per degree centigrade rise
of temperature.
(d) Dalton’s law of partial pressures: Partial pressure of a gas or of saturated vapors is the pressure which it would exert if
contained alone in the entire confined given space.
P= p1+p2+p3+……..
nRT/V = p1+p2+p3+……..
(e) Grahm’s law of diffusion: Grahm’s law of diffusion states thatthe rate of diffusion of gases varies inversely as the square root of
the density of gases.
R∝1/√ρor R1/R2 =√ρ2/ ρ1
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So, a lighter gas gets diffused quickly.
(f) Avogadro’s law:It states that under similar conditions of pressure and temperature, equal volume of all gases contain equal
number of molecules.
For m gram of gas, PV/T = nR = (m/M) R
Pressure of a gas (P):P = 1/3 (M/V) C2 = 1/3 (ρ) C2
• Root mean square (r.m.s) velocity of the gas:Root mean square velocity of a gas is the square root of the mean of the squares of
the velocities of individual molecules.
C= √[c12+ c22+ c32+…..+ cn2]/n = √3P/ ρ
• Pressure in terms of kinetic energy per unit volume:The pressure of a gas is equal to two-third of kinetic energy per unit
volume of the gas.
P= 2/3 E
• Kinetic interpretation of temperature:Root mean square velocity of the molecules of a gas is proportional to the square root of
its absolute temperature.
C= √3RT/M
At, T=0, C=0
Thus, absolute zero is the temperature at which all molecular motion ceases.
• Kinetic energy per mole of gas:
K.E. per gram mol of gas = ½ MC2 = 3/2 RT
• Kinetic energy per gram of gas:
½ C2 = 3/2 rt
Here, ½ C2 = kinetic energy per gram of the gas and r = gas constant for one gram of gas.
• Kinetic energy per molecule of the gas:
Kinetic energy per molecule = ½ mC2 = 3/2 kT
Here, k (Boltzmann constant) = R/N
Thus, K.E per molecule is independent of the mass of molecule. It only depends upon the absolute temperature of the gas.
(a) Most probable speed:It is the speed, possessed by the maximum number of molecules of a gas contained in an enclosure.
Vm= √[2kT/m]
(b) Average speed (Vav):Average speed of the molecules of a gas is the arithmetic mean so the speeds of all the molecules.
Vav= √[8kT/πm]
(c) Root mean square speed (Vrms):It is the square root of the mean of the squares of the individual speeds of the molecules of a gas.
Vrms = √[3kT/m]
Vrms >Vav >Vm
• Degree of Freedom (n):Degree of freedom, of a mechanical system, is defined as the number of possible independent ways, in
which the position and configuration of the system may change.
In general, if N is the number of particles, not connected to each other, the degrees of freedom n of such a system will be,
n = 3N
If K is the number of constraints (restrictions), degree of freedom n of the system will be,
n = 3N –K
• Degree of freedom of a gas molecule:
(a)Mono-atomic gas: Degree of freedom of monoatomic molecule, n = 3
(b)Di-atomic gas:
At very low temperature (0-250 K): Degree of freedom, n = 3
At medium temperature (250 K – 750 K): Degree of freedom, n = 5 (Translational = 3, Rotational = 2)
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At high temperature (Beyond 750 K): Degree of freedom, n = 6 (Translational = 3, Rotational = 2, Vibratory =1), For calculation
purposes, n = 7
• Law of equi-partition of energy: In any dynamical system, in thermal equilibrium, the total energy is divided equally among all
the degrees of freedom and energy per molecule per degree of freedom is ½ kT.
E = ½ kT
• Mean Energy:Kinetic Energy of one mole of gas is known as mean energy or internal energy of the gas and is denoted by U.
U = n/2 RT
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Practice Questions 1. Which of the following is a measure of hotness of a body?
(a) Temperature (b) Heat
(c) specific head (d) Latent heat
2. A glass of ice-cold water left on a table on a hot summer
day eventually warms up whereas a cup of hot tea on the
same table cools down because.
(a) its surrounding media are different
(b) the direction of heat flow depends on the
surrounding temperature with respect to the object
(c) the variation of the resistance of a wire with
temperature
(d) All of the above
3. The ice point and the steam point of water are two
convenient fixed points and are known as the
(a) cooling point and heating point, respectively
(b) heating point and cooling point, respectively
(c) freezing point and boiling point, respectively
(d) boiling point and freezing point, respectively.
4. At the freezing and boiling points.
(a) pure water freezes and boils under standard
pressure, respectively
(b) salty water freezes and boils under standard
pressure respectively
(c) Both (a) and (b)
(d) neither (a) nor (b)
5. A fully inflated balloon shrinks when it is put into cold
water, because.
(a) water causes lesser pressure from outside on the
balloon.
(b) water causes a pull on balloon which presses it
(c) air inside the balloon contracts due to cooling
(d) rubber of balloon expands on cooling and
compresses air inside.
6. When water boils or freezes, during these processes its
temperature
(a) increases
(b) decreases
(c) does not change
(d) sometimes increases & sometimes deceases
7. Steam burns are more serious as
(a) steam at 100°C carries same heat as that of water
100°C but pressure of steam is more.
(b) steam is more reactive.
(c) steam has less surface tension and so it burns surface
more rapidly
(d) steam at 100°C carries more heat than water at
100°C
8. A point at which vaporisation curve, fusion curve and
sublimation curve meet, is called.
(a) melting point (b) boiling point
(c) freezing point (d) triple point
9. Triple point of water is
(a) 273.16 K temperature and 1 atm pressure.
(b) 273.16 K temperature and 6.11×10-3 atm pressure.
(c) 4°C temperature and 76 cm of Hg pressure
(d) STP
10. Hot water or milk when left on a table begins to cool
gradually, because
(a) temperature of surroundings is higher
(b) everything cools down with time irrespective of the
temperature of the surroundings
(c) temperature of surroundings is lesser.
(d) None of the above
11. The rate of loss of heat depends on
(a) the sum of temperature of the body and its
surroundings
(b) the difference of the body and its surroundings
(c) the product of temperature of the body and its
surroundings
(d) the ratio of temperature of the body and its
surroundings.
12. On a hilly region, water boils at 95°C. The temperature
expressed in Fahrenheit is
(a) 100°F (b) 20.3°F
(c) 150°F (d) 203°F
13. When the pressure is held constant, the volume of a
quantity of the gas is related to the temperature as V/T =
constant. This is known as
(a) Boyle’s law
(b) Dalton partial pressure law
(c) Charles law
(d) Ideal gas equation
14. Measurements on real gases deviate from the values
predicted by the ideal gas law at
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(a) high temperature (b) low temperature
(c) room temperature (d) All of these
15. The absolute minimum temperature for an ideal gas,
therefore inferred by extrapolating the straight line to
the temperature axis, is called as
(a) Kelvin temperature
(b) Celsius temperature
(c) low temperature
(d) absolute zero
16. When temperature of water is raised from 0°C to 4°C, it
(a) expands
(b) contracts
(c) expands upto 2°C and then contracts upto 4°C
(d) contract upto 2°C and then expands upto 4°C
17. Which of the following graph shows the variation of
volume of water with increase in temperature?
18. Temperature of atmosphere is Kashmir falls below –
10°C in winter. Due to this water animal and plant life of
Dal-lake
(a) is destroyed in winters
(b) frozen is winter and regenerated in summers
(c) survives as only top layer of lake in frozen
(d) None of the above
19. When water changes to ice, the temperature of system
(water ⇌ ice)
(a) decreases
(b) increases
(c) remains same
(d) state change has no relation with temperature
20. When water changes to water vapour, then
(a) no temperature change takes place
(b) no heat flow occurs
(c) heat flows into the water from surrounding heat
source
(d) Both (a) and (c)
21. Time taken to heat water upto a temperature of 40°C
(from room temperature) is t1 and time taken to heat
mustard oil (of same mass and at room temperature)
upto a temperature of 40°C is t2, then (given mustard oil
has smaller heat capacity)
(a) t1 = t2
(b) t1> t2
(c) t2> t1
(d) t1 and t2 both are less than 10 min
22. Amount of heat required to warm an object depends on
(a) mass of object
(b) temperature change
(c) nature of substance
(d) All of these
23. A good coolant must have
(a) low specific heat (b) high specific heat
(c) low density (d) high density
24. A block of ice at 0°C is slowly heated and converted into
steam at 100°C. Which of these curves represents the
phenomenon qualitatively?
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25. At atmospheric pressure, water boils at 100°C. If
pressure is reduced, then
(a) it still boils at same temperature
(b) it now boils at a lower temperature
(c) it now boils at a higher temperature
(d) it does not boil at all
26. A liquid boils when its vapour pressure is equal to
(a) 6.0 cm of Hg column
(b) atmospheric pressure
(c) double of atmospheric pressure
(d) 1000 Pa or more
27. Cooking is difficult on hills because
(a) atmospheric pressure is higher
(b) atmospheric pressure is lower
(c) boiling point of water is reduced
(d) Both (b) and (c)
28. Change of state from solid to vapour state without
passing through the liquid state is called
(a) regelation (b) sublimation
(c) condensation (d) sedimentation
29. The latent heat of vaporization of a substance is always
(a) greater than its latent heat of fusion
(b) greater than its latent heat of sublimation
(c) equals to its latent heat of sublimation
(d) less than its latent heat of fusion
30. For the phase diagram of water given in figure, curves
OA, AB and AC are respectively?
(a) Sublimation curve, vaporization curve and fusion
curve
(b) Sublimation curve, fusion curve and vaporization
curve
(c) Fusion curve, vaporization curve and Sublimation
curve,
(d) Fusion curve, Sublimation curve and vaporization
curve
31. The amount of heat that a body can absorb by radiation.
(a) depends on colour and temperature both of body.
(b) depends on colour of body only
(c) depends on temperature of body only
(d) depend on density of body
32. The bottoms of utensils for cooking food are blackened
to
(a) absorb minimum heat from fire
(b) absorb minimum heat from fire
(c) emit radiation
(d) reflect heat to surroundings
33. A liquid in a beaker has temperature θ(t) at time t and θ0
is temperature of surroundings, then according to
Newton’s law of cooling, the correct graph between loge
= (θ – θ0) and t is
34. Specific heat capacity of a substance depends on
I. mass of substance. II. Nature of substance.
III. rise in temperature IV. Volume of substance.
(a)I and II (b) II and III
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(c) III and IV (d) I and IV
35. During vaporization,
I. the change of state from liquid to vapour state occurs.
II. the temperature remains constant.
III. both liquid and vapour states coexist in equilibrium.
IV. specific heat of substance increases.
Correct statements are
(a) I, II and IV (b) II, III and IV
(c) I, III and IV (d) I, II, III and IV
36. Which of the following statement(s) is/are correct?
I. Gases are poor thermal conductors.
II. Liquids have conductive intermediate between solids
and gases.
III. Heat conduction can take place from cold body to
hotter body.
(a) Only I (b) Only II
(c) Only III (d) Both I and II
37. Which of the following statement(s) is/are correct?
I. Convection is a mode of heat transfer by actual motion
of matter.
II. Convection is possible only in gases.
III. Convection can be natural of forced.
(a) Only I (b) Both I and III
(c) Only II (d) All of these
38. The common example of forced convection system are
I. human blood circulatory system.
II. cooling system of an automobile engine.
III. human-liver system.
IV. water cycle.
(a) Only I (b) Both I and II
(c) I, II and IV (d) Both II and III
39. Which of the following statement(s) is/are correct?
I. Thermos bottle consists of a double-walled glass vessel
with inner and outer walls coated with silver.
II. In flask, space between the walls is evacuated to
reduced conduction and convection losses.
III. Thermos bottle is useful for preventing hot contents
(like milk) from getting cold or to store cold content (like
ice).
(a) Only I (b) Only II
(c) Both I and II (d) All of these
40. Which of the following statement(s) is/are correct?
I. Conduction of heat takes places in solids and liquids
like mercury and molten metals.
II. In radiation energy directly flows from heat source to
the given body at a speed of 3 × 108 ms-1.
III. Convection of heat takes place in liquids only.
(a) Only I (b) Both II and III
(c) Only III (d) Both I and II
41. Match Column I and Column II as per the anomalous
behavior of water and choose the correct options from
codes given.
Column I Column II
A. Density maximum 1. 4°C
B. Volume increases 2. 27°C to 10°C
C. Volume decreases 3. 4°C to 0°C
D. Density increases 4. 0°C to 4°C
A B C D A B C D
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(a) 1 3 2 4 (b) 1 2 3 4
(c) 1 4 3 2 (d) 1 4 2 3
42. If there is a rise in temperature θ, then time period of
pendulum
(a) increases (b) decreases
(c) no change (d) cannot be determined
43. A sphere, a cube and a thin circular plate, all of same
material and same mass are initially heated to same high
temperature.
(a) Plate will cool faster cube the slowest
(b) Sphere will cool fastest and cube the slowest
(c) Plate will cool fastest and sphere the slowest
(d) Cube will cool fastest and plate the slowest
44. Gulab jamuns (assumed to be spherical) are to be heated
in an oven. They are available in two size, one twice
bigger (in radius) than the other. Pizzas (assumed to be
discs) are also to be heated in oven. They are also in two
sizes, one twice bigger (in radius) than the other. All four
are put together to be heated to over temperature.
Choose the correct option from the following.
(a) Both size gulab jamuns will get heated in the same
time
(b) Smaller gulab jamuns are heated before bigger ones
(c) Smaller pizzas are heated before bigger ones
(d) Bigger pizzas are heated before smaller
45. Interatomic forces are
(a) attractive in long range
(b) repulsive in short range
(c) negligible in gases
(d) All a, b and c
46. According to atomic hypothesis
(a) atoms attract each other when they are little distance
apart
(b) atoms repel if they being squeezed into one another
(c) Both (a) and (b)
(d) Neither (a) nor (b)
47. Choose the correct option.
(a) Avogadro's law with Dalton theory could explain Gay
Lussac's law
(b) Dalton's atomic theory could also be termed as
molecular theory as well
(c) Initially Dalton's theory was not accepted by other
scientists
(d) All of the above
48. Which of the following option is correct about the flow of
a liquid?
(a) In liquids the atoms are not as rigidly fixed as in solid
(b) In liquids the atoms are more rigidly fixed as in gas
(c) In liquid the separation between atoms arespaced
about Å
(d) All of the above
49. A real gas behaves like an ideal gas if its
(a) pressure and temperature are both high
(b) pressure and temperature are both low.
(c) pressure is high and temperature is low
(d) pressure is low and temperature is high.
50. Kinetic theory of gases
(a) correctly explains specific heat capacities of many
gases
(b) relates properties of gases such as viscosity ,
conduction etc., with molecular parameters
(c) Both (a) and (b) are correct.
(d) None of these
51. Choose the correct option.
(a) Maxwell and Boltzmann were among the scientists
who developed kinetic theory
(b) Kinetic theory gives molecular interpretation of
pressure and temperature of a gas
(c) Kinetic theory is consistent with gas laws and
Avogardro's hypothesis
(d) All of the above
52. The collisions of the molecules of an ideal gas are
(a) elastic (b) inelastic
(c) total KE and total momentum remains conserved
(d) Neither total KE nor total momentum is conserved.
53. Choose the correct option.
(a) In derivation of pressure the shape of vessel doesn't
matter.
(b) Pressure of gas in equilibrium is same everywhere
(c) In derivation of pressure we neglect the collisions
between the molecules as it doesn't make much
difference
(d) All of the above
54. The internal energy of ideal gas is in form of
(a) kinetic energy of molecules
(b) potential energy of molecules.
(c) both kinetic and potential energy of molecules
(d) gravitational potential energy of molecules
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55. According to the kinetic theory of gases, the temperature
of a gas is measure of average
(a) velocities of its molecules
(b) linear momenta of its molecules
(c) kinetic energies of its molecules
(d) angular momenta of its molecules
56. The internal energy of an ideal gas depends on
(a) pressure (b) volume
(c) mass (d) temperature
57. The mass of 22.4L of O2 at STP is
(a) 32 kg (b) 16 g (c) 32 g (d) 16 mg
58. Which one of the following graphs represents the
behavior of an ideal gas?
59. Match the following.
Column I Column II
A. pV = kBNT 1. Gay-Lussac’s law
B. p ∝ 1/V
T = constant
2. Boyle’s law
C. p ∝ T
V = constant
3. Ideal gas equation
D. V ∝ T
p = constant
4. Charles’ law
A B C D A B C D
(a) 3 2 1 4 (b) 3 3 1 4
(c) 3 2 4 1 (d) 3 2 1 4
60. Which of the following diagrams (figure) depicts ideals
gas behavior?
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ANSWER KEY
1 A 2 B 3 C 4 A 5 C
6 C 7 D 8 D 9 B 10 C
11 B 12 D 13 C 14 B 15 D
16 B 17 B 18 C 19 C 20 D
21 B 22 D 23 B 24 D 25 B
26 B 27 D 28 B 29 A 30 B
31 A 32 B 33 A 34 B 35 D
36 D 37 B 38 B 39 D 40 D
41 A 42 A 43 C 44 BC 45 D
46 C 47 D 48 A 49 D 50 C
51 D 52 A 53 D 54 A 55 C
56 D 57 C 58 D 59 D 60 AC
SOLUTION
1. (a) Temperature is a measure of hotness of a body. A body at
a higher temperature when touched gives a feeling of
more hotness than that at a lower temperature. But,
temperature does not give the measure of content of
heat in a body.
2. (b) When the temperature of body, ice cold water or hot tea
in this case, and its surrounding medium are different,
then heat transfer take place between the system and the
surrounding medium, until the body and the
surrounding medium are at the same temperature
3. (c) The ice point and the steam point of water are two
convenient fixed points and known as the freezing and
boiling points. These two points are the temperature at
which pure water freezes and boils respectively under
standard pressure.
4. (a) On the freezing and boiling points, pure water freezes
and boils respectively under standard pressure.
5. (c) Air inside the balloon contracts and therefore balloon
walls shrink. A change in temperature of a body causes a
change in dimensions.
6. (c) When water boils or freezes, its temperature does not
change during these processes. Heat is absorbed or
librated as latent heat.
7. (d) For water, the latent heat of fusion and vaporization are
Lf = 3.33 × 105 J kg-1 and Lv = 22.6 × 105 J kg-1,
respectively. That is 3.33 × 105 J of heat is needed to melt
1 kg of ice at 0°C, and 22.6 × 105 J of heat is needed to
convert 1 kg of water to steam at 100°C. This is why
burns from steam are usually more serious than those
from boiling water.
8. (d) At triple point matter exists in all three states,
i.e., vapour state, solid state and liquid state.
9. (b) Triple point of water is 273.16 K temperature and 6.11 ×
10-3 atm pressur.
10. (c) Hot water or milk when left on a table begins to cool
gradually because it loses the heat to the surroundings.
11. (b) The rate of loss of heat depends on the difference in
temperature between the body and its surroundings.
12. (d) Given, C = 95°C, F = ?
Using relation 32
,180 100
F C we get
32 95
9 5
F
⇒F – 32 = 171⇒F = 171 + 32 = 203°F
13. (c)
14. (b) Measurements on real gases deviation from the values
predicted by the ideal gas law at low temperature. But,
the relationship is linear over a large temperature range,
and it looks as though the pressure might reach zero
with decreasing temperature, if the gas continued to be a
gas.
15. (d) The absolute minimum temperature for an ideal gas,
therefore, inferred by extrapolating the straight line to
the temperature axis, as in figure. This temperature is
found to be – 273.15°C and is designated as absolute
zero.
16. (b) Water contracts when it is heated from 0°C to 4°C, its
volume is least at 4°C.
17. (b) Water contracts when is heated from 0°C to 4°C.
Thus, its density increases. Density of water is maximum
at 4°C. when the water is further heated, it expands and
volume thus increases.
18. (c) Ice formed floats over surface, it exerts pressure over
water below causing lowering of freezing point and ice
layer on top also acts like an insulator. Bottom of lake
remains in liquid state due to above reason.
19. (c) During state change, the temperature of the system
remains same.
20. (d) When water boils or freezes, its temperature does not
change during these processes but heat transfer takes
place.
21. (b) Time taken to heat mustard oil is much less than that
required by the same amount of water for the same rise
in temperature.
22. (d) The quantity of heat required to warm a given substance
depends on its mass m, the change in temperature ΔT
and the nature of substance.
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23. (b) Water has the highest specific heat capacity compared to
other substances. For this reason, water is used as a
coolant in automobile radiators as well as a heater is hot
water bags.
Owing to its high specific heat capacity, the water warms
up much slowly, than the other liquids.
24. (d) A plot of temperature versus time showing the changes
in the state of ice on heating (not to scale).
O → A : Solid + liquid
A → B : liquid
B → C : liquid + gas
C → D : gas
25. (b) When pressure is increased, boiling point is elevated. i.e.,
at higher pressure, water boils at temperature greater
than 100°C. similarly, at reduced pressure, water boils at
a lower temperature.
26. (b) When vapour pressure is equal to atmosphere pressure,
then boiling occurs.
27. (d) At high altitudes, atmospheric pressure is lower,
redacting the boiling point of water as compared to that
at sea level. When boiling point of water is reduced, it
has lesser heat at boiling, it transfers lesser heat to raw
food material, per unit time. So, it takes more time to
cook food.
On the other hand, boiling point is increased inside a
pressure cooker by increasing the pressure. Hence,
cooking is faster.
28. (b) Sublimation is conversion of a solid into vapour without
being liquid.
29. (a) As more energy is required for enormous expansion.
When a substance is changed from liquid to gaseous
state, latent heat of vaporization is always greater than
latent heat of fusion.
30. (b) The point on the sublimation curve OA represents states
in which the solid and vapour phases coexist. Points on
the fusion curve AB represent states in which solid and
liquid phase coexist.
31. (a) The thermal radiation that falls on a body partly
reflected and partly absorbed. The amount of heat that a
body can absorb, by radiation depends on the colour of
the body and temperature of body.
32. (b) Black bodies absorb and emit radiant energy better than
bodies of lighter colours. The bottoms of the utensils for
cooking food are blackened so that they absorb
maximum heat from the fire and give it to the vegetables
to be cooked.
33. (a) According to Newton’s law of cooling, rate of fall in
temperature is proportional to the difference in
temperature of the body with surroundings, i.e.
-d
dt
= h (θ – θ0)
⇒0
dk dt
⇒In (θ – θ0) = -kt + C
Which is a straight line with negative slope.
34. (b) If ΔQ stands for the amount of heat absorbed or rejected
by a substance of mass m when it undergoes a
temperature change ΔT, then the specific heat capacity of
that substance is given by
C =1 Q
m t
The specific heat capacity is the property of the
substance which determines the change in the
temperature of the substance (undergoing no phase
change) when a given quantity of heat is absorbed (or
rejected) by it. Also, specific heat of vapour state is more
than that of liquid state.
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35. (d) The change of state from liquid to vapour (for gas) is
called vaporisatin. It is observed that when liquid is
heated, the temperature remains constant until the
entire amount of the liquid is converted into vaopur.
That is, both the liquid and vapour states of the
substance coexist in thermal equilibrium, during the
change of state from liquid to vapour. The temperature
at which the liquid and the vapour states of the
substance coexist is called its boiling point.
36. (d) Gases are poor thermal conductors while liquids have
conductivities intermediate between solids and gases.
Conduction takes place from hot to cold body.
37. (b) Convection is a mode of heat transfer by actual motion of
matter. It is possible only in fluids. Convection can be
natural or forced. In natural convection, gravity plays an
important part.
38. (b) The common examples of forced convection system are
forced-air heating system in home, the human
circulatory system and the cooling system of an
automobile engine.
In the human body, the heart acts as the pump that
circulates blood through different parts of the body,
transferring heat by forced convection and maintaining it
at a uniform temperature.
39. (d) In thermos bottle, radiation from the inner wall is
reflected back into the contents of the bottle. The outer
wall similarly reflects back any incoming radiation. The
space between the walls is evacuated to reduce
conduction and convection losses and the flask is
supported on an insulator like cork.
The device is, therefore useful for preventing hot
contents (like milk) from getting cold or alternatively to
store cold contents (like ice).
40. (d) Three modes of heat transmission are conduction,
convection and radiation.
S.
No.
Conduction Convection Radiation
1. There is no
bodily
motion of
medium
particles.
Medium
particles
vibrate to
and fro
about their
mean
positions
and pass on
Heat is
transferred
from one
part of
system to
another by
the actual
motion of
the
particles of
the system.
Medium has no
role as thermal
radiations are
transmitted
without any
material
medium.
thermal
energy to the
neighbouring
particles.
2. Conduction
of heat takes
place in
solids and
liquids like
mercury and
molten
metals.
Convection
of heat
takes place
in fluids,
i.e., liquids
as well as
gases.
Radiant energy
directly flows
from heat
source to the
given body at a
speed of 3 × 108
ms-1 as
electromagnetic
waves.
41. (a) Density of water is maximum at 4°C ⇒ A → 1.
∴ Voltage decreases when water is cooled from 27°C to
10°C. Also, if water is heated from 0°C to 4°C, its density
increases and volume decreases C → 4 and D → 4.
Volume increases when water is cooled down from 4°C
to 0°C ⇒ B → 3. Also, density decreases from 4°C to 0°C.
42. (a) Given, time period of a simple pendulum
T = 2πl
g i.e.,T ∝ l
since, when temperature is increased, length of the
pendulum increases and hence, the time period
increases.
43. (c) Consider the diagram where all the three objects are
heated to same temperature T. We know that density, =
mass
volume
volume will also be same.
As thickness of the plate is least hence, surface area of
the plate is maximum.
We know that according to Stefan’s law of heat loss H ∝
AT4
where, A is surface area for object and T is temperature.
Hence,Hsphere :Hcube : Hplate
= A sphere : A cube : A plate
As A plate is maximum.
Hence, the plate will cool fastest.
As, the sphere is having minimum surface area hence, the
sphere cools slowest.
44. (b, c) Smaller gulab jamuns are having least surface area
hence, they will be heated first.
As in case of smaller gulab jamun heat radiated will be
less.
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Similarly, smaller pizzas are heated before bigger ones
because they are of small surface areas.
45. (d) Interatomic forces are attractive in long range and
repulsive in short range and negligible in gases.
46. (c) Atoms attract when they are little distance apart and
repel, if they being squeezed into one another.
47. (d) Avogadro’s law say Equal volumes of all gases at equal
temperature and pressure have the same number of
molecules. Avogadro’s law, when combined with
Dalton’s theory explains Gay Lussac’s law. Dalton’s
atomic theory can also be referred to as the molecular
theory of matter. The theory is now well accepted by
scientists. However even at the end of the nineteenth
century there were famous scientist who did not believe
in atomic theory.
48. (a) In liquids the atoms not as rigidly fixed as in solid, and
can move around. The enables a liquid to flow.
49. (d) A real gas behaves like an idea gas at low pressure and
high temperature.
50. (c) Kinetic theory of gases correctly explains specific heat
capacities of many gases and it relates properties of
gases viscosity, conduction etc., with molecular
parameter.
51. (d) The kinetic theory was developed in the nineteenth
century by Maxwell, Boltzmann and others. It has been
remarkably successful. It gives a molecular
interpretation of pressure and temperature of a gas is
consistent with gas laws and Avogadro’s hypothesis.
52. (a) According to kinetic theory of gases the collision among
molecules and the collision of molecules with the walls of
container are elastic.
53. (d) The collision of molecules will not make any difference in
the expression of pressure because
(i) the distribution of velocities will not change even
after collision as gas is in steady state.
(ii) we find 2
xv , so by taking average we reduce the
change of error.
54. (a) As in an ideal gas molecular interaction is negligible, the
concept of potential energy of molecular will not work
here. So, the internal energy will depend only on the
kinetic energy of the molecules.
55. (c) According to kinetic theory of gases the temperature of a
gas is a measure of the average kinetic energies of the
molecules of the gas.
56. (d) Internal energy of an ideal gas depends only on the
temperature of the gas.
57. (c) The mass of 22.4 L of any substance at STP is equal to its
molecular weight in grams.
So, M (O2) = 32 g
58. (d) For an ideal gas keeping the temperature same
throughout,
pV = constant
hence, for a given mass, the graph between pV and V will
be a straight line parallel to V-axis whatever may be the
volume.
59. (d) According to Boyle’s law p1V1 = p2V2 = constant.
According to Charles’ law 1 2
1 2
V V
T T = constant. Also,
according to ideal gas equation p1V1 = kNT.
60. (a, c) We know that ideal gas equation is
pV = nRT … (i)
(a) When pressure, p = constant
From Eq. (i) volume V ∝ Temperature T
(b) When T = constant
From Eq. (i) pV = constant
(c) When V = constant.
From Eq. (u) p ∝ T
So, the graph is straight line passes through the origin.
(d) From Eq. (i) pV ∝ T
⇒ pV
T= constant ⇒ So, the graph hence, through origin.
SSC CDS
BANKrAILWAY
ª Concepts with Visual Understanding
ª Core Physics (Detailed Theory)
Physics
ª Practical Applications of Physics
ª Previous year Questions from
1999 to till date
C L A S S E S
Chapter - 18
(Hydrostatics & Hydrodynamics)
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HYDROSTATICS AND HYDRODYNAMICS Pressure
The force acting per unit area on a surface is known as
pressure.
Pressure (p) = Force (F)
Area (A)
It is a scalar quantity having SI unit Nm–2 or Pascal
(Pa).
Fluid is the name given to a substance which begins to flow when external force is applied on it.
Pressure in Liquid
The pressure at any point inside the liquid acts in all directions. Pressure at a depth h in a liquid of density p is given by
P = pgh + P0
where, g = acceleration due to gravity
p = density of liquid
h= height of liquid column
and P0 = atmospheric pressure.
Floatation and swimming in sea water is easier due to its high density than fresh water.
At higher altitudes, atmospheric pressure is lower than that at sea level.
Archimedes' Principle
It states that when a body is immersed wholly or partly in a liquid at rest, it loses some of its weight. The loss in weight of the body
in the liquid is equal to the weight of the liquid displaced by the immersed part of the body.
Note: The upward force exerted by a fluid on the immersed body is called buoyant force or buoyancy or upthrust.
Density
The ratio of mass m to the volume V of a body is called its density (i.e. mass present in its unit volume). It is a scalar quantity having
SI unit - kg/m3.
The density of water is 1000 kg/m3 (at 40C).
Density (p) = Mass (m)
Volume (V)
Law of Floatation
When a body of density , volume V is immersed completely in a liquid of density , two
forces are acting on it.
1. True weight W (= V g) of the body acting vertically downwards through the centre of
gravity.
2. Buoyant force or upward thrust w (= V g), equal to the weight of the liquid displaced,
acting vertically upward through the centre of Buoyancy.
The observed weight of the body immersed into the liquid = W – w = V g – V g.
If W > w, then W – w is positive. In this case, the body will sink to the bottom of the liquid.
If the body is not hollow from inside, then the density of solid body is greater than the
density of liquid (i.e., >).
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If W < w, then W – w is negative. In this case, the body will rise above the surface of liquid to such an extent that the weight of the
liquid displaced by the immersed part of the body (i.e., upward thrust) becomes equal to the weight of the body. The body then will
float. In this case the density of solid body is less than the density of liquid (i.e., <).
If W = w, then W – w = 0. It means the resultant force acting on the body fully immersed in the liquid in zero. In this case, the body
is at rest anywhere within the liquid. The apparent weight of the body is zero at all positions inside the liquid. In this situation, the
body will float if its whole volume is just immersed in the liquid. If the body is solid then the density of body is equal to the density
of liquid (i.e., = ).
Thus the law of floatation states that a body will float in a liquid, if weight of the liquid displaced by the immersed part of the body
is atleast equal to or greater than the weight of the body.
There will be equilibrium of floating bodies if the following conditions are fulfilled.
(i) A body can float if the weight of the liquid displaced by the immersed part of body must be equal to the weight of the body.
(ii) A body can be in equilibrium if the centre of gravity of the body and centre of buoyancy must be along the same vertical line.
(iii) The body will be in stable equilibrium if centre of gravity of body lies vertically below the centre of buoyancy and in the
unstable equilibrium if centre of gravity lies vertically above the centre of buoyancy.
1. When an ice block is floating in water in a vessel, then the level of water in the vessel will not change when the whole ice melts into
water.
2. When an ice block is floating in a liquid in a vessel and ice completely melts, then the following cases may arise for the level of
liquid in the vessel.
(i) If density of liquid is greater than that of water, i.e., l>w, the level of liquid plus water will rise.
(ii) If density of liquid is less than the density of water, i.e., l<w, the level of liquid plus water will decrease.
(iii) If density of liquid is equal to the density of water, i.e., l = w, the level liquid plus water will remain unchanged.
Atmospheric Pressure
The air that envelopes the earth is called atmosphere and the pressure exerted by it on a body on the earth is called atmospheric
pressure.
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The atmospheric pressure is maximum at the surface of the earth and goes on decreasing as we move up into the earth's
atmosphere. The measurement of atmospheric pressure is carried out by barometer.
Barometers are also used for weather forecasting. If the barometric height falls suddenly, it indicates the coming of a storm. A
gradual fall and rise in barometric height indicate the possibility of rain and fair weather respectively.
1 atmospheric pressure = 1.01 bar = 1.01 × 105 N/m2
A barometer is a device for measuring atmospheric pressure.
Pascal's Law
It states that if gravity of effect is neglected, the pressure at every point of
liquid in equilibrium of rest is same.
This law also accounts for the principle of transmission of pressure in
liquids or gases. In this form,
Pascal's law states that the increase in pressure at one point of the
enclosed liquid in equilibrium of rest is transmitted equally to all other
points of the liquid and also to the walls of the container, provided the
effect of gravity is neglected.
i.e P1 = P2
This applies to fluid at rest
Surface Tension
Thus, surface tension is the property of the liquid by virtue of which the free surface of liquid at rest
tends to have minimum surface area and as such it behaves as if covered with a stretched membrane.
Measurement of Surface Tension
Surface tension of a liquid is measured as the force acting on unit length of a line imagined to be drawn
tangentially anywhere on the free surface of the liquid at rest. It acts at right angles to this line on both
the sides and along tangent to the liquid surface.
S = F/l
Units of surface tension are dyne/cm in cgs system and Nm–1 in SI.
The dimensional formula of surface tension is [ML°T–2]. Surface tension is a scalar quantity because it has no specific direction for
a given liquid.
Illustrations of Surface Tension
1. Rain drops are spherical in shape because each drop tends to acquire minimum surface area due to surface tension, and for a given
volume, the surface area of sphere is minimum.
2. When mercury is split on a clean glass plate, it forms globules. Tiny globules are spherical on account of surface tension because
force of gravity is negligible.
3. When a greased iron needle is placed gently on the surface of water at rest, so that it does not prick the water surface ,the needle
floats on the surface of water despite its being heavier.
The weight of the needle is balanced by the vertical components of the forces of surface tension. If the water surface is pricked by
one end of the needle, the needle sinks down.
Surface tension of a liquid decreases with an increase in temperature.
Surface Energy
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The potential energy of the molecules in the surface of liquid is called the surface energy.
Surface energy = T × ΔA
where, T = surface tension of liquid
ΔA = increase in surface area
Surface Film
It is the top most layer of liquid at rest with thickness equal to the molecular range.
Inter-Molecular Forces
The forces between the molecules of the substances are called intermolecular forces.
Types of Intermolecular Forces
There are two types of intermolecular forces.
(i) Force of Adhesion or Adhesive Force
It is the fore of attraction acting between the molecules of different substances.
Water wets the surface of a glass container. While writing, graphite from lead pencil sticks to
the paper on account of adhesive forces. Fevicol, cement etc are useful in glueing two surface.
(ii) Force of Cohesion or Cohesive Force
It is the force of attraction amongst the molecules of the same substance.
The solids have definite shape and size. It is due to strong forces of cohesion amongst their
molecules. Liquids have definite volume, but no definite shape. Therefore, cohesive forces in
case of liquids are lesser. Hence, cohesive forces amongst the molecule of a gas are minimum.
Mercury does not wet the surface of a glass container because the force of cohesion amongst
molecules of mercury is stronger than the force of adhesion between molecules of mercury and
glass.
The cohesive and adhesive forces are Vander Waal forces. These forces are different from
ordinary gravitational forces and do not obey inverse square law. The cohesive or adhesive
force varies inversely as the seventh power of distance between the molecules, i.e., the cohesive or adhesive force increases rapidly
with decrease in distance between the molecules.
Detergent and Surface Tension
The dirty greasy stains on the clothes cannot be cleared by simply washing the clothes in water. This is so because water does not
find its contact with greasy dirt and hence cannot wet such surfaces. By adding detergent or soap to water, the greasy dirt from
cloth can be easily cleaned.
(i) The molecules of the soap or detergent are hair pins shaped.
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(ii) When soap or detergent is dissolved in water, then heads of the hair pins shaped molecules get attracted to water surface.
(iii) When clothes with greasy stains are dipped in detergent or soap mixed water, then the pointed ends of the hair pins shaped
molecules get attached to the molecules of the greasy stain. As a result of it, the water comes into contact with greasy stain and thus
a water greasy dirt interface is formed. Due to it, the greasy dirt is held suspended. It happens so because detergent molecules
reduce the surface tension between water and greasy stain.
(iv) When clothes are rinsed in water, then the greasy dirt is washed away by the running water.
Applications of Surface Tension
1. Since surface tension of soap solution is low, it can spread over large area. Hence it can wash clothes more effectively. Hot soap
solution proves still better as surface tension decreases further on heating.
2. For the same reason, surface tension of all lubricating oils and paints is kept low.
3. Stormy waves at sea are calmed by pouring oil on sea water.
4. In soldering, addition of 'flux' reduces the surface tension of molten tin, hence, it spreads.
5. Anticeptics like dettol have low surface tension, so they spread faster.
Capillarity
A tube with a fine and uniform bore throughout its length is called a capillary tube.
The phenomenon of rise or fall of liquid in a capillary tube is called capillarity.
Rise or fall of a liquid in a capillary tube is caused by surface tension and depends on the
relative magnitude of cohesion of the liquid and the adhesion of the liquid to the walls of the
containing vessel.
Liquids rise in tubes if they wet (adhesion > cohesion)
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Liquids fall in tubes that do not wet (cohesion > adhesion).
Applications of capillary action
(i) The fine pores of a blotting paper act like capillary tubes. Ink rise in them leaving the paper dry.
(ii) A towel soaks water on account of capillarity action.
(iii) Oil rises in the long narrow spaces between the threads of a wick, because they act as fine capillaries.
(iv) Swelling of wood in rainy season, is due to rise of moisture from air, in the pores of wood.
(v) Ploughing of field is essential for preserving moisture in the soil. By ploughing, the fine capillaries in the soil are broken. Water
from within the soil shall not rise and evaporate off.
(vi) Sand is drier soil than clay. This is because holes between the sand particles are not so fine as compared to that of clay, as to
draw up water by capillarity action.
Piezometer: For measuring pressure inside a vessel or pipe in which liquid is there, a tube may be attached to the walls of
the container (or pipe) in which the liquid resides so liquid can rise in the tube. By determining the height to which liquid rises and
using the relation P = ρgh, gauge pressure of the liquid can be determined. Such a device is known as piezometer. To avoid capillary
effects, a piezometer's tube should be about 1/2 inch or greater.
Fluid
A fluid is a substance which deforms continuously under the action of shearing forces, however small they may be. Conversely, it
follows that:
If a fluid is at rest, there can be no shearing forces acting and, therefore, all forces in the fluid must be perpendicular to the planes
upon which they act.
Shear stress in a moving fluid
Although there can be no shear stress in a fluid at rest. Shear stresses are developed when the fluid is in motion. If the particles of
the fluid move relative to each other so that they have different velocities, causing the original shape of the fluid to become
distorted. If, on the other hand, the velocity of the fluid is same at every point, no shear stresses will be produced, since the fluid
particles are at rest relative to each other.
The differences between the behaviors of solids and fluids under an applied force are as follows:
(i) For a solid, the strain is a function of the applied stress, providing that the elastic limit is not exceeded. For a fluid, the rate of strain
is proportional to the applied stress.
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(ii) The strain in a solid is independent of the time over which the force is applied and, if the elastic limit is not exceeded, the
deformation disappears when the force is removed. A fluid continues to flow as long as the force is applied and will not recover its
original form when the force is removed.
Fluid vs gas
Although liquids and gases both share the common characteristics of fluids, they have many distinctive characteristics of their own.
A liquid is difficult to compress and, for many purposes, may be regarded as incompressible. A given mass of liquid occupies a fixed
volume, irrespective of the size or shape of its container, and a free surface is formed if the volume of the container is greater than
that of the liquid.
A gas is comparatively easy to compress. Changes of volume with pressure are large, cannot normally be neglected and are related
to changes of temperature. A given mass of gas has no fixed volume and will expand continuously unless restrained by a containing
vessel. It will completely fill any vessel in which it is placed and, therefore, does not form a free surface.
Types of Fluids
1. Newtonian fluids:
Fluids which obey the Newton's law of viscosity are called as Newtonian fluids. Newton's law of viscosity is given by
τ = μ dv/dy
where τ = shear stress
μ = viscosity of fluid
dv/dy = shear rate, rate of strain or velocity gradient
All gases and most liquids which have simpler molecular formula and low molecular weight such as water, benzene, ethyl alcohol,
CCl4, hexane and most solutions of simple molecules are Newtonian fluids.
2. Non-Newtonian fluids:
Fluids which do not obey the Newton's law of viscosity are called as non-Newtonian fluids.
Generally non-Newtonian fluids are complex mixtures: slurries, pastes, gels, polymer solutions etc.,
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Various non-Newtonian Behaviors:
Time-Independent behaviors:
Properties are independent of time under shear.
Bingham-plastic: Resist a small shear stress but flow easily under larger shear stresses. e.g. tooth-paste, jellies, and some slurries.
Pseudo-plastic: Most non-Newtonian fluids fall into this group. Viscosity decreases with increasing velocity gradient. e.g. polymer
solutions, blood. Pseudoplastic fluids are also called as Shear thinning fluids. At low shear rates(du/dy) the shear thinning fluid is
more viscous than the Newtonian fluid, and at high shear rates it is less viscous.
Dilatant fluids: Viscosity increases with increasing velocity gradient. They are uncommon, but suspensions of starch and sand
behave in this way. Dilatant fluids are also called as shear thickening fluids.
Physical properties of fluid
1. Viscosity:
The viscosity (μ) of a fluid measures its resistance to flow under an applied shear stress. Representative units for viscosity are
kg/(m.sec), g/(cm.se (c) (also known as poise designated by P). The centipoise (cP), one hundredth of a poise, is also a
convenient unit, since the viscosity of water at room temperature is approximately 1 centipoise.
The kinematic viscosity (v) is the ratio of the viscosity to the density:
Viscosity of liquids:
Viscosity of liquids in general, decreases with increasing temperature.
The viscosities (μ) of liquids generally vary approximately with absolute temperature T according to:
ln = a - b ln T
Viscosity of gases:
Viscosity of gases increases with increase in temperature.
The viscosity () of many gases is approximated by the formula:
= o(T/To)n
in which T is the absolute temperature, o is the viscosity at an absolute reference temperature To, and n is an empirical exponent
that best fits the experimental data.
The viscosity of an ideal gas is independent of pressure, but the viscosities of real gases and liquids usually increase with pressure.
Viscosity of liquids are generally two orders of magnitude greater than gases at atmospheric pressure. Fow example, at 25oC,
water = 1 centipoise and air = 1 x 10-2centipoise.
2. Vapor pressure:
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The pressure at which a liquid will boil is called its vapor pressure. This pressure is a function of temperature (vapor pressure
increases with temperature). In this context we usually think about the temperature at which boiling occurs. For example, water
boils at 100oC at sea-level atmospheric pressure (1 atm abs). However, in terms of vapor pressure, we can say that by increasing
the temperature of water at sea level to 100oC, we increase the vapor pressure to the point at which it is equal to the atmospheric
pressure (1 atm abs), so that boiling occurs. It is easy to visualize that boiling can also occur in water at temperatures much below
100oC if the pressure in the water is reduced to its vapor pressure. For example, the vapor pressure of water at 10oC is 0.01 atm.
Therefore, if the pressure within water at that temperature is reduced to that value, the water boils. Such boiling often occurs in
flowing liquids, such as on the suction side of a pump. When such boiling does occur in the flowing liquids, vapor bubbles start
growing in local regions of very low pressure and then collapse in regions of high downstream pressure. This phenomenon is called
as cavitation
3. Compressibility and the Bulk modulus
All materials, whether solids, liquids or gases, are compressible, i.e. the volume V of a given mass will be reduced to V - V when a
force is exerted uniformly all over its surface. If the force per unit area of surface increases from p to p + p, the relationship
between change of pressure and change of volume depends on the bulk modulus of the material.
Bulk modulus (K) = (change in pressure) / (volumetric strain)
Volumetric strain is the change in volume divided by the original volume. Therefore,
(change in volume) / (original volume) = (change in pressure) / (bulk modulus)
i.e., -V/V = p/K
Negative sign for V indicates the volume decreases as pressure increases.
the concept of the bulk modulus is mainly applied to liquids, since for gases the compressibility is so great that the value of K is not
a constant.
Equation of continuity
A
b
a2, v2
a1, v1 Cross-sectional view of a pipe through which incompressible liquid is passing,
then Equation of continuity states that
volume of liquid entering = volume of liquid leaving
a1v1 = a2v2
a1 area of tube at point A
v1velocity of liquid at point A
a2area of tube at point B.
v2velocity of liquid at point B.
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Practice Questions 1. The key property of fluids is that
(a) they offer very little resistance to shear stress
(b) their shape changes.
(c) they offer very large resistance to shear stress
(d) Both (a) and (b)
2. Average pressure pav is defined as
(a) av
Fp
A (b) av
Vp
F
(c) av
Ap
F (d)
av
Fp
V
3. Pressure is a ……. quantity.
(a) scalar (b) vector
(c) tensor (d) Either (a) or (c)
4. Dimensions of pressure are
(a) [ML –1T-2] (b) [ML2 T2]
(c) [ML 3T-1] (d) [M2L-1T-2]
5. If two liquids of same masses but densities 1 and
2
respectively are mixed, then density of mixture is given
by
(a) 1 2
2
(b) 1 2
1 22
(c) 1 2
1 2
2
(d) 1 2
1 2
6. If two liquids of same volume but different densities 1
and 2 are mixed, then density of mixture is given by
(a) 1 2
2
(b) 1 2
1 22
(c) 1 2
1 2
2
(d) 1 2
1 2
7. Pascal's law states that pressure in a fluid at rest is the
same at all points, if
(a) They are at the same height
(b) They are along same plane
(c) They are along same line
(d) Both (a) and (b)
8. Pressure is applied to an enclosed fluid. It is
(a) Increased and applied to very part of the fluid
(b) Diminished and transmitted to the walls of the
container
(c) Increased in proportion to the mass of the fluid and
then transmitted
(d) transmitted unchanged to every portion of the fluid
and the walls of container.
9. Pressure is applied to an enclosed fluid. It is
(a) Increased and applied to every part of the fluid
(b) diminished and transmitted to the walls of the
container
(c) increased in proportion to the mass of the fluid and
then transmitted
(d) transmitted unchanged to every portion of the fluid
and the walls of container
10. In a streamline flow,
(a) the speed of a particle always remains same.
(b) the velocity of a particle always remains same
(c) the kinetic energies of all the particles arriving at a
given point are the same.
(d) the potential energies of all the particles arriving at a
given point are the same
11. In a laminar flow, the velocity of the liquid in contact
with the walls of the tube is
(a) zero (b)maximum
(c) in between zero and maximum
(d) equal to critical velocity
12. We have three beakers A, B and C containing three
different liquids. They are stirred vigorously and placed
on a table. Then, liquid which is
(a) most viscous comes to rest at the earliest.
(b) most viscous comes to rest at the last.
(c) most viscous slows down earliest but comes to rest at
the last.
(d) All of them come to rest at the same time.
13. For a surface molecule,
(a) the net force on it is zero
(b) there is a net downward force
(c) the potential energy is less than that of a molecule
inside
(d) the potential energy is more than that of a molecule
inside.
14. Pressure is a scalar quantity, because
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(a) it is the ratio of force to area and both force and area
are vectors.
(b) It is the ratio of the magnitude of the force to area
(c) It is the ratio of the component of the force normal to
the area.
(d) It does not depend on the size of the area chosen.
15. With increase in temperature, the viscosity of
(a) gases decreases (b) liquids increases
(c) gases increases (d) liquids decreases
16. Streamline flow is more likely for liquids with
(a) high density (b) high viscosity
(c) low density (d) low viscosity
17. The density of water at 40C is
(a) 1.0 × 103 kgm-3 (b) 4 × 102 kgm-3
(c) 6 × 103 kgm-3 (d) 3.2 × 103 kgm-3
18. As the temperature of water increases, its viscosity
(a) remains unchanged
(b) decreases
(c) increases
(d) increases or decreases depending on the external
pressure
19. Surface tension is due to
(a) frictional forces between molecules
(b) cohesive forces between molecules
(c) adhesive forces between molecules
(d) Both (b) and (c)
20. The value of surface tension of water is minimum at
(a) 4°C (b) 25°C
(c) 50°C (d) 75°C
21. The surface tension of a liquid at its boiling point
(a) because zero
(b) becomes infinity
(c) is equal to the value at room temperature
(d) is half to the value at the room temperature
22. Why are drops and bubbles spherical?
(a) Surface with minimum energy
(b) Surface with maximum energy
(c) High pressure
(d) Low pressure
23. Match physical quantities in Column I with their
dimensions given in Column II
Column I Column II
A. Coefficient of
viscosity
1. [ML0T-2]
B. Density 2. [M0L0T0]
C. Surface tension 3. [ML-1T-1]
D. Reynold’s number [ML-3T0]
A B C D A B C D
(a) 2 3 4 1 (b) 1 3 4 3
(c) 3 4 1 2 (d) 1 2 3 4
24. Match the following Column I and Column II.
Column I Column II
A. Hydraulic lift 1. Archimedes’
principle
B. A razor blade can be
made to float on water
surface in a tray.
2. Pascal’s law
C. The dam of water
reservoir is made thick
at the bottom level.
3. Surface tension
D. Ship is floating on
ocean water.
4. Pressure
A B C D A B C D
(a) 2 3 4 1 (b) 2, 4 3 4 1
(c) 4 1 3 4 (d) 4,1 2 3 4
25. Which of the following diagrams does not represent a
streamline flow?
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ANSWER KEY
1 D 2 A 3 A 4 A 5 C
6 A 7 A 8 D 9 D 10 B
11 A 12 A 13 BD 14 BC 15 CD
16 BC 17 A 18 B 19 D 20 A
21 A 22 A 23 C 24 A 25 D
SOLUTION 1. (d) The key property of fluids is that they offer very little
resistance to shear stress. So, their shape changes by
application of very small shear stress.
2. (a) If F is the magnitude of the normal force acting over an
area A, then the average pressure p is defined as the
normal force acting per unit area.
Pav =F
A
3. (a) Pressure is a scalar quantity. It is the component of the
force normal to the area under consideration and not the
(vector) force that appear in the numerator.
4. (a) Dimensions of pressure are [ML-1T-2]. The SI unit of
pressure is Nm-2.
5. (c) =1 2
1 2
2 2
1 1
Total mass m m
Total volume V V
∴ = 1 2
1 2
2
6. (a) = 1 21 2 1 2mass
2 2 2
Vm mTotal
Total volume V V
7. (a) Pascal’s law states that pressure in a fluid at rest is the
same at all points if they are at the same height.
8. (d) Pascals’ law
p =F
A= gh
∴ It does not depend on the weight of fluid.
9. (d) Pascals’ law
p =F
A= gh
∴ It does not depend on the weight of fluid.
10. (b) Both speed and direction of flow remain same.
11. (a) Most viscous fluid comes to rest quickly due to
dissipation of energy at a larger rate.
12. (a) Most viscous fluid comes to rest quickly due to
dissipation of energy at a larger rate.
13. (b, d)
Consider the diagram where two molecules of a liquid
are shown. One is well inside the liquid and other is on
the surface. The molecule (A) which is well inside
experiences equal forces from all directions, hence net
force on it will be zero.
And molecules on the liquid’s surface have some extra
energy as it surrounded sustained by only lower half side
of liquid molecules.
14. (b, c)
Pressure is defined as the ratio of magnitude of
component of the force normal to the area and the area
under consideration. As magnitude of component is
considered, hence it will not have any direction. So,
pressure is a scalar quantity.
15. (c, d) For liquids’ coefficient of viscosity, ∝1
T
i.e., with increase in temperature decreases.
For gases coefficient of viscosity, ∝ T
i.e., with increase in temperature increases.
16. (b, c) Streamline flow is more likely for liquids having low
density. We know that greater the coefficient of viscosity
of a liquid more will be velocity gradient hence each line
of flow can be easily differentiated. Also higher the
coefficient of viscosity lower will be Reynold’s number,
hence flow will be more likely to be streamline.
17. (a) The density of water at 40C (277 K) is 1.0 × 103 kgm3.
18. (b) For liquids, viscosity decreases with temperature.
19. (d) Both cohesive and adhesive forces result in surface
tension.
20. (a) Value of surface tension decreases with increase in
temperature.
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21. (a) Surface tension is zero at boiling point.
22. (a) A liquid air interface has energy, so for a given volume
the surface with minimum energy is the one with the
least area.
23. (c) Density is mass per unit volume. Its dimension are [ML-
3T0].
The coefficient of viscosity has dimensions [ML-1T-1].
Reynold’s number is a dimensions number.
Surface tension is force per unit length. Hence, its
dimensions are [M L0T-2] Hence,
A → 3, B → 4, C → 1, D → 2
24. (a) A → 2, B → 3; C → 4; D → 1
Column I Column II
A. Hydraulic lift 2. Pascal’s law
B. A razor blade can be
made to float on water
surface in a tray
3. Surface tension
C. The dam of water
reservoir is made thick
at the bottom level
4. Pressure
D. Ship is floating on
ocean water
1. Archimedes’
principle
25. (d) In a streamline flow at any given point, the velocity of
each passing fluid particles remains constant. If we
consider a cross-sectional area, then a point on the area
cannot have different velocities at the same time, hence
two streamlines of flow cannot cross each other.
SSC CDS
BANKrAILWAY
ª Concepts with Visual Understanding
ª Core Physics (Detailed Theory)
Physics
ª Practical Applications of Physics
ª Previous year Questions from
1999 to till date
C L A S S E S
Chapter - 19
(Mechanical Properties of Solid)
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MECHANICAL PROPERTIES OF SOLIDS Matter is anything that has mass and occupy space. It includes all the physical 'material' around us. Different matter have dissimilar
properties such as elasticity, density, viscosity, etc., to distinguish them from each other.
Stress
The restoring force per unit area is called stress. Its units is N/m2 or Pascal.
Stress = Restoring force (F)
Area (A)
There are different types of stress given as below
Normal Stress/Longitudinal Stress
Stress produced normal to the axis of the body is called normal stress. It consists of two types.
1. Compressive Stress: Stress produced in the body, which is responsible for the compression in the body is called compressive
stress.
2. Tensile Stress: Stress produced in the body, which is responsible for the elongation in the body is called tensile stress.
Shearing Stress and Volumetric Stress
Stress produced along the axis of the body under the action of a force parallel to its axis, i.e. tangential force is called shearing
stress. It is also called tangential stress.
Stress produced in the body under the action of the force, which is perpendicular to the surface and proportional to the area in case
the body is immersed in fluid, is called volumetric stress.
Strain
When a system of forces acts on a body, it undergoes some deformation. This deformation per unit length is known as unit strain or
simply a strain.
Strain is a ratio of change in dimension to the original dimension, it has no units or dimensional formula.
Strain = Changeinlength( l)
Original length (l)
There are three types of strain given as below
1. Longitudinal Strain:It is the ratio of change in length to that of initial length of the body (i.e. ΔL/L).
Force perpendicular to Area A must be considered when equal & opposite
force is applied on both ends. Then length increases.
Longitudinal Stress Pressure units
= = arF
Area
= Force perpendicular to Area
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Longitudinal strain = l change in length
l Original length
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2. Shear Strain
The angle between the displaced state and initial state of the body is called shearing strain. x
i.e.l
Force is applied parallel to surface
Shear stress = Force actingparallel to area F
Area A
E, Shear strain () = x
tanl
G, shear modules = Stress F l F
strain A x A
tan
3. Volumetric strain: It is the ratio of change in volume of the body to its initial volume (i.e. ΔV/V).
Volume Stress, P (Extra Pressure) = F
Area
Volume Strain, E = V
V
Bulk Modulus, B =Normal stress
volumetric strain=
F / a
V / V
Negative Sign is used because volume decreases once volumetric stress is applied.
Poisson's Ratio
When an object is streched, volume remains same so length but area (diameter )
Longitudinal strain =l Change in length
l Original length
Lateral strain =d Change in diameter
d Original diameter
It is the ratio of lateral strain to the longitudinal strain in a streched wire.
Poisson's ration (μ) = Lateral strain
Longitudinal strain=
d / d
l / l
Length , diameter
It is a dimensionless quantity.
Poisson's ratio for steel is 0.30.
Elasticity
The property of matter by virtue of which a body tends to regain its original shape and size after the removal of deforming force is
called elasticity.
If the body completely regains its original shape after removal of deforming force, the body is called perfectly elastic body.
Plasticity
The property of matter by virtue of which it does not regain its original shape and size after removal of deforming force is called
plasticity. If the body remains in deformed shape even after removal of the deforming force, it is called perfectly inelastic or
plastic body.
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Note: Steel is more elastic than rubber because the magnitude of stress for a given strain is much large in steel than rubber.
Perfectly Plastic: Putty, mud, Paraffin Wax
Perfectly Elastic: Quartz,Phospher Bronze
Elastomer These are the materials which possess the qualities such as
• Stress vs Strain is not a straight line.
• Elastic Region is large.
• Ex. Rubber
Hooke's Law
According to this law,
within the elastic limits, the stress is directly proportional to the strain produced in a body.
i.e. Stress ∝ Strain or Stress = E × Strain
Stress
Strain= E
where, E is a constant called as Modulus of Elasticity (Proportionality constant)
It states that the extension produced in the wire is directly proportional to the load
applied, within elastic limit.
i.e., within elastic limit, extension load applied.
There are three Modulus of elasticity given as below
Young's Modulus of Elasticity (Y)
It is defined as the ratio of longitudinal stress to the longitudinal strain within the elastic limit. Thus,
Y = Longitudinal stress
Longitudinal strain
The SI unit of Young's modulus of elasticity is Nm-2 or Pascal (denoted by P a and in CGS system is dyne/cm2.
Bulk Modulus of Elasticity (B)
It is defined as the ratio of normal stress to the volumetric strain within the elastic limit. Thus,
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B = Normal stress
Volumetric strain
The SI unit of bulk modulus of elasticity is Nm-2 or pascal (denoted by Pa and in CGS system is dyne/cm2.
Modulus of Rigidity (ɳ)
It is defined as the ratio of shearing stress to the shearing strain within the elastic limit. It is also called shear modulus of rigidity.
Thus, ɳ = Shearing stress
Shearing Strain
The SI unit of ɳ is Nm-2 or Pascal (denoted by P and in CGS system is dyne/cm2.
Note: Elastic hysteresis has an important application in shock absorbers.
Elastic Hysteresis. When a deforming force is applied on a body, then the strain does not change
simultaneously with stress, rather it lags behind the stress. The lagging of strain behind the stress is
defined as elastic hysteresis.
Stress-Strain Graph
• Upto Point A Proportional limit
Slope of this graph gives us Modulus of Elasticity , Hooke's Law is obeyed in this
region.
• A to B Elastic property of material is retained i.e. if you will remove stress,
material will regain its shape.
• B Elastic limit or yield limit
y Yield Stress: The value of stress on whose application we get yield point.
• After B If you stress, there is a much increase in strain & stress, if will
remove stress, material will not gain its original position.
• So, At C Object is permanently reformed at strain Permanent Set.
• After CSmall increase in stress gives larger value of strain.
• Dultimate Tensile strength
After this if we stress, strain .
• a point after D,At E fracture point object break.
If there is very small gap or No gap between D & E Object is brittle
If there is large gap between D & E Object is Malleable (sheets) and Ductile (wires)
Strain Energy = F e
2 ;
F maximum force acting on object
e elongation of object due to force
Strain energy volume = Stress Strain
2
E
8
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Practice Questions 1. The property of a body by virtue of which it tends to
regain its original size and shape of a body when applied
force is removed, is known as
(a) fluidity (b) elasticity
(c) plasticity (d) rigidity
2. In solids, inter-atomic forces are
(a) totally repulsive
(b) totally attractive
(c) combination of (a) and (b)
(d) None of these
3. Elasticity is shown by materials because inter-atomic or
inter –molecular forces
(a) increases when a body is deformed
(b) decreases when a body is deformed
(c) remains same when a body is deformed
(d) becomes non-zero when a body is deformed.
4. The nature of molecular forces resembles with the
nature of the
(a) gravitational forces (b) nuclear force
(c) electromagnetic force (d) weak force
5. Elasticity is due to
(a) decreases of PE with separation between
atoms/molecules
(b) increases of PE with separation between
atoms/molecules
(c) asymmetric nature of PE curve
(d) None of the above
6. For a perfectly rigid body,
(a) Young's modulus is infinite and bulk modulus is zero
(b) Young's modulus is zero and bulk modulus is infinite.
(c) Young's modulus is infinite and bulk modulus is also
infinite
(d) Young's modulus is zero and bulk modulus is also
zero.
7. Statement I Elongation produced in a body is directly
proportional to the applied force.
Statement II This law of elasticity, now called as Hooke’s
law.
(a) Both Statement I and Statement II are correct and
Statement II is the correct explanation of Statement I.
(b) Both Statement I and Statement II are correct but
Statement II is not the correct explanation of Statement I.
(c) Statement I is correct but Statement II is incorrect.
(d) Statement I is incorrect but Statement II is correct.
8. Match the following Column I and Column II
Column I Column II
A. Longitudinal stress 1. Volume changes
B. Shear stress 2. Shape changes
C. Bulk stress 3. Volume does not
change
D. Tensile stress 4. Shape does not
change
A B C D
(a) 1, 4 2,3 1,4 1,4
(b) 2,3 1,4 1,4 1,4
(c) 1 4 1,4 2,3
(d) 2,3 4,1 4 1
9
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9. Match the following Column I and Column II. More than
one match are possible.
Column I Column II
A. Young’s modulus of a
substance
1. Depends on
temperature
B. Bulk modulus of a
substance
2. Depends of length
C. Modulus of rigidity of
a substance
3. Depends on area of
cross-section
D. Volume of a
substance
4. Depends on the
nature of material
A B C D
(a) 1,4 1,4 1,4 1,2,3
(b) 1,2 3,2 4,1 1,3,4
(c) 1 3 4 2
(d) 1 4 3 2
10. From the graph, we can see in the region from O to A, the
curve is linear. In this region, Hooke’s law is obeyed.
Thus, from O to A, the solid body behaves as a/an
(a) elastic body (b) partially elastic body
(c) plastic body (d) inelastic body
11. The point B in the curve is known as
(a) yield point (b) elastic limit
(c) plastic limit (d) breaking point
12. Modulus of rigidity of ideal liquid is
(a) infinity
(b) zero
(c) unity
(d) some finite small non-zero constant value
ANSWER KEY
1 B 2 C 3 D 4 C 5 C
6 C 7 A 8 A 9 A 10 A
11 A 12 B
SOLUTION 1. (b) The property of a body, by virtue of which it tends to
region its original size and shape when the applied force
is removed, is known as elasticity and the deformation
caused is known as elastic deformation.
2. (c) Inter-atomic forces are attractive, when atoms are far
from each other and it becomes repulsive when atoms
come very close.
3. (d) When a body is deformed, atoms/ molecules are
displaced from their equilibrium positions (F = 0) and as
a result there is a force (F ≠ 0) acts to restore them.
4. (c) Inter-molecular and inter-atomic forces are due to
electric and magnetic interactions between atoms and
molecules.
5. (c) Elasticity occurs due to asymmetric nature of U versus
graph.
When separation of molecules is less than (or more than)
equilibrium separation, PE of system increases and
system dissipated this energy to reach minimum energy
configuration.
As a result separation is again restored to equilibrium
separation for which U is minimum.
6. (c) For a perfectly rigid body, both young's modulus and
bulk modulus is infinite.
7. (a) Robert Hooke, an English physicist performed
experiments on springs and found that the elongation
(change in the length produced in a body is proportional
to the applied force or load. In 1676, he presented his
law of elasticity, now called Hooke’s law.
8. (a) Longitudinal or tensile stress causes change of length so
volume changes but shape does not change. Shear causes
change of shape Bulk stress causes change of volume.
A → (1,4), B → (2,3), C → (1,4), D → (1,4)
9. (a) A → (1,4), B → (1,4), C → (1,4), D → (1,2,3)
A. Young’s modulus of substance depends on
temperature and nature of material.
B. Bulk modulus of a substance depends on temperature
and nature of material.
C. Modulus of rigidity of a substance depends on
temperature and nature of material.
D. Volume of substance depends on temperature, length
and area of cross-section.
10. (a) In this region, Hooke’s law is obeyed. The body regions
its original dimensions when the applied force is
removed. The solid behave as an elastic body.
11. (a) In the region from A to B, stress and strain are not
proportional. Nevertheless, the b….. still returns to its
original dimension when the load is removed The point
B in the curve is known as yield point (also known as
elastic limit) and the corresponding stress is known as
y) of the material.
12. (b) No viscous force exists in case of ideal fluid, hence
tangential forces are zero so there is no stress develop.
SSC CDS
BANKrAILWAY
ª Concepts with Visual Understanding
ª Core Physics (Detailed Theory)
Physics
ª Practical Applications of Physics
ª Previous year Questions from
1999 to till date
C L A S S E S
Chapter - 20
(Relativity)
1
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THEORY OF RELATIVITY By Albert Einstein in 1915
When speed of object approaches the speed of light (c). Its M, L, T(mass, length, time) shows a different behavior.
Einstein mass energy relation
E = mc2
Etotal energy =KE + Rest mass energy
mc2 = (r – 1) moc2 + moc2
KE = mc2 – moc2 r = 2 2
1
1 v / c
KE = (m – mo)c2
i.e. Decrease in mass is converted into kinetic energy(KE).
Relation between TE(total energy), Rest mass energy & momentum
E2 = p2c2 + 2 4
om c
Decrease in mass converted to kinetic energy
m = o
2 2
m
1 c
mo rest mass of body.
m mass of body movingwith velocity n comparable to speed of light(c)
Length Contraction
L = O 2 2
1L
1 v / c
c speed of light
v velocity of object
LO length in stationary frame
L length in moving frame (moving with velocity c)
2
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Time Dilation
t = o
2 2
t
1 v / c
t actual time that appears to stationary man on earth
to time of clock in moving object.
Note: Earth is not an inertial frame because of its orbital and rotational motion but for most of the purposes, earth may be
regarded as an inertial frame of Reference.
A frame of reference consists of an abstract coordinate system and the set of physical reference points that uniquely fix
the coordinate system and standardize measurements
Types of Frame of Reference
Inertial/unaccelerated System
Newton's 1st law holds.
Non-Inertial/Accelerated System
Newton's 1st law does not holds.
Transformations
These are used to convert variables from one frame of reference to another frame of reference.
Transformations
Galileon Transformation if v < c
t' = t
Lorentz Transformation if v >> c
Due to invariance of speed of light in all inertial frames
t' t
v- speed of an object moving in inertial frame
c – speed of light
t- time period
t'- observed time period in another frame of reference
In a Lorentz Transformation, A circle appears to be an ellipse in a frame f' which is moving with velocity v relative to
frame f.
Postulates of Special Theory of Relativity
1. All fundamental laws of physics retain the same form in all the inertial frames of reference.
2. The velocity of light in free space is constant and is independent of relative motion of source and observer.
Michelson-Morley Exp.
Purpose: To confirm the existence of luminiferous ether as stationary.
OR
To find velocity of earth with respect to ether.
3
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