284 DGT ' MCQ Worksheet ' Heat and Thermodynamics 11. Heat and Thermodynamics Revision Notes : IMPORTANT FORMULAE, FACTS AND TERMS Relation between different scales of temperatures (i) C T 0 100 = F T 32 180 = R T 0 80 = K T 273.15 100 (ii) T C = 5 9 (T F – 32) (iii) F C 9 T T 32 5 Faulty Thermometer False reading - lower point Range = True reading - lower point Range 1. Expansion of Solids. Almost all the solids expands on heating. This due to increase in their interatomic distances with rise in temperature. Expansion may be in length, surface area or volume of the solid. (i) Coefficient of linear expansion It is defined as the increase in length of solid per unit original length per unit degree rise in temperature. l = .T l SI units of are k –1 . T l l or l' = l (1 + T ) (ii) Coefficient of superficial expansion It is defmed as the increase in area per unit original area per unit degree rise in temperature. S ST S' = S (1 + T ). (iii) Coefficient of cubic expension It is defined as the increase in volume of solid per unit original volume per unit degree rise in temperature. V VT or V' = V (1 + T ). 2. Expansion of Liquids. The coefficient of expansion of liquid is defmed as the increase in volume of liquid per unit original volume per degree rise in temperature. DGT Group - Tuitions (Feed Concepts) XIth – XIIth | JEE | CET | NEET | Call : 9920154035 / 8169861448
Transcript
284DGT ' MCQ Worksheet ' Heat and Thermodynamics
11. Heat and Thermodynamics
Revision Notes :
IMPORTANT FORMULAE, FACTS AND TERMS
Relation between different scales of temperatures
(i) CT 0
100
= FT 32
180
= RT 0
80
= KT 273.15
100
(ii) TC =
5
9(T
F – 32)
(iii) F C
9T T 32
5
Faulty Thermometer
False reading - lower point
Range = True reading - lower point
Range
1. Expansion of Solids. Almost all the solids expands on heating. This due to increase in their interatomicdistances with rise in temperature. Expansion may be in length, surface area or volume of the solid.(i) Coefficient of linear expansion
It is defined as the increase in length of solid per unit original length per unit degree rise intemperature.
l=
. T
l
SI units of are k–1.
T l l
or l' = l (1 + T )
(ii) Coefficient of superficial expansionIt is defmed as the increase in area per unit original area per unit degree rise in temperature.
S
S T
S' = S (1 + T ).
(iii) Coefficient of cubic expensionIt is defined as the increase in volume of solid per unit original volume per unit degree rise intemperature.
V
V T
or V' = V (1 + T ).
2. Expansion of Liquids. The coefficient of expansion of liquid is defmed as the increase in volume ofliquid per unit original volume per degree rise in temperature.
3. Expansion of Gases. Volume coefficient of expansion of gas is defmed as the increase in volume of
the gas per unit original volume per degree rise in temperature at constant pressure.
v
V
V T
Similarly pressure coefficient of expansion of gas is defined as the increase in pressure of the gas perunit original pressure per degree rise in temperature at constant volume
P
P
P T
The value of Y
v or Y
P is same equal to 273 per degree celsius.
4. Latent Heat. It is defmed as the amount of heat required to change the state of unit mass ofsubstance without increase in temperature. It is denoted by L.Latent heat of fusion or melting for ice is 80 cal g–1.Latent heat of vapourisation for water is 540 cal g–1.
5. Specific Heat. It is defmed as the amount of heat required to raise the temperature of unit mass ofsubstance through 1°C. It is denoted by C.
C = Q
m T
Its S.I. units are J kg–1 k–1
For water C = 1 cal g–1 °C–1
For ice C = 0.5 cal g–1 °C–1
TWO SPECIFIC HEATS OF GASThe two specific heats of gas are1. Motar specific heat at constant volume (C
v)
It is defmed at the amount of heat required to raise the temperature of 1 mole of the gas through1°C at constant volume.
2. MOLAR SPECIFIC HEAT AT CONSTANT PRESSURE (CP)
It is defmed as the amount of heat required to raise temperature of 1 mole of the gas through1°C at constant pressure.The realtion between two specific heats of gas isC
P – C
V = R
6. P–V Diagram. It is graph showing the variation of pressure withchange in volume 1 during a thermodynamic process. It is alsocalled indicator diagram. Work done during a w thermodynamicprocess is equal to area under the P– V diagram. Work done ispositive if volume increases and is taken as negative if volumedecreases.
7. Cyclic Process. It is defmed as the process in which the systemreturns to its initial stage after under going number of changes.Work done during a cyclic process is equal to area under the closedloop.If the loop is traced clockwise then work done is positive and if theloop is traced anti–clockwise the work done is negative.
8. Degrees of Freedom. The total number of coordinates orindependent quantities 1 which must be known in order to describe
completely the state of system is called degrees of freedom of the system. Total number of differentways by which a system can acquire energy is called degrees of freedom. It is denoted by f.(i) Monoatomic Gases
The gases like He, Ar, Ne etc. are monoatomic gases and only prossess translatory motion.Therefore, for monotomic gas at all temperature.
f = 3(ii) Diatomic Gases
The gases such H2, N
2, O
2 etc. are diatomic gases. Depending upon the temperature they can
possess different types of motion.(a) At T < 70 K, the diatomic gases have only translatory motion.
Thus f = 3 for T < 70 K(b) At 250 K < T < 750 K, the diatomic gases have translatory motion and rotational motion.
f = 3 + 2 = 5, For 250 K < T < 750 K.(c) For T > 5000 K, diatomic gas molecular possess translational, rotational and vibratory
motion.Thus, f = 3 + 2 + 2 = 7 for T > 5000 K
(iii) Triatomic GasesThe gases such as SO
2, H
2S etc. are triatomic gases.
For linear triatomic molecular.f = 7
and for non–linear triatomic moleculef = 6
9. Law of Equipartition of Energy. It states that for a dynamical system in thermal equilibrium theenergy is distributed equally amongest its various degrees of freedom and the energy associated with
each degree of freedom is 1
2 kT. where k = Boltzman's constant. 1·38 × 10–23 J mole–1 K–1)
If a gas molecule possess f degrees of freedom, then energy of one molecule
= f × 1
2 KT..
One mole of a gas contains Avogadro's number (N) atoms or molecules.Thus energy of 1 mole of gas is
U = N × f × 1
2 KT = f
1
2RTT
Cv =
dU Rf
dT 2
As CP = C
v + R
CP =
R ff . R 1 R
2 2
pC
rC
r = 2
1f
10. Internal Energy. The internal energy of the gas is defined as the sum of the kinetic energy which isfunction of temperature of gas and the intermolecular potential energy of the gas molecules which isfunction of volume of the gas. Thus internal energy of a real gas is both function of its temperatureand volume of the gas.
For an ideal gas there is no attraction between the molecules and hence it does not possess intermolecular potential energy. Thus for an ideal gas the internal energy is purely kinetic and function ofonly temperature of the gas.
11. First Law of Thermodynamics. It is based on law of conservation of energy. It states that whensome heat dQ is given to the system then a part of it is used in increasing the internal energy by dUand the remaining part is used in doing external work dW.It dQ, dU and dW are in same units then
dQ = dU + dW12. Work done during an Isothermal Process. The work done in an isothermal process for n mole of
gas when its volume changes from V1 to V
2 is
W = 2·303 nRT log10
2
1
V
V
W = 2·303 nRT log10
1
2
P
P
13. Work done during an Adiabatic Process. Work done in adiabatic change for 1 moleis W = R
1 [T
1 – T
2]
Where T1 = initial temperature of gas.
T2 = final temperature of gas.
Also W = cv (T
1 – T
2) where c
v is specific heat of gas at constant volume.
Also W = 1
1 [P1V
1 – P
2V
2]
14. Slopes of Adiabatic and Isothermal Curve. dP
dV gives the slope of a adiabatic or isothermal curve.
For isothermal process PV = Const.
PdV + V dP = 0.
dP P
dV V
For adiabatic process
PV = Const.
P. VP–1dV + V dP = 0
dP P
dV V
Slope of adiabatic process
Slope of isothermal proces = P / V
P / V
Since p
v
C
C is always greater than 1. Thus, we find from the figure that slope of adiabatic curve is
more than that of isothermal curve.15. Carnot's Reversible Cycle. In this engine heat Q
1 is absorbed from source at high temperature
T1. A part Q
2 of this heat is rejected to sink at lower temperature T
Efficiency of heat engineIt is defined as the ratio work done by the engine to the heat absorbed by it.
1
W
Q
1 2
1
Q Q
Q
2
1
Q1
Q
Since2
1
Q
Q = 2
1
T
T
2
1
T1
T
16. Refrigerator. A refrigerator may be considered as a carnot engine working in reverse direction.Here amount of heat Q
2 is removed from sink at lower temperature T
2 by doing external work W and
heat Q1 is rejected to source at higher temperature T
1.
Thus Q2 + W = Q
1 W = Q1 – Q
2
Coefficient of performanceIt is defined as the ratio of amount of heat removed from sink at lower temperature T
2 to the work
done W in removing this heat.
2 2 2
1 2 1 2
Q Q T
W Q Q T T
In Focus :
1. Relation between different scales of temperature
C FT 0 T 32
100 180
= RT 0
80
= KT 273.15
100
2. Charge in temp C K 95 F 3. – 40°C has same value on Ce1cius and
Fahrenheit scales.4. Melting point of solids which contract on melting
decreases with in crease in pressure e.g. iv orcast iron whereas melting point of solids whichexpand on melting increase with increase inpressure e.g. wax, glass etc.
5. Boiling point increases with increase in pressure.6. Faulty Thermometer.
False reading - lower point
range
True reading - lower point
range
7. Co–efficient of linear expansion
=T
l
l
l' = l(1 + T )
8. Coefficient of superficial expansion
S
S T
S' = S(1 + T )
9. Coefficient of cubic expansion
V
V T
V' = V(1 + T )
10. Relation between and
6 = 3 = 2
or = 2 3
11. Heat supplied to a solid of mass m for increasing
temperature T is Q = mC T..12. Heat supplied to change its state at constant
temperature Q = mL.13. Gases possess infinite values of specific heat but
2. The number of degrees of freedom for a mole ofdiatomic gas at N.T.P. is :a) 30.1 × 1023 b) 18.01 × 1023
c) 30.1 × 1021 d) None of the above.3. The ratio of slope of adiabatic to that of an
isothermal process is :
a) 1
b)
c) – 1 d) None of the above.
4. A Carnot's engine operates with a source at500 K & sink at 375 K The engine consumes600 k cal of heat in one cycle, the heat rejectedto sink per cycle is:a) 250 k calb) 350 k calc) 450 k cald) 550 k cal.
5. Two identical samples of a gas expands so thatvolume is doubled. The first sample undergoesisothermal expansion while the second isexpanded adiabatically. The final pressure:a) in first sample is greaterb) in second sample is greaterc) equal in both samplesd) nothing can be said.
6. A reversible Camot's engine is working between260K and 300K It takes 500 cal of heat fromsink. Heat rejected to the source at higher temp.for this refrigerator is :a) 400 calb) 477 calc) 377 cald) 577 cal.
7. One mole of an ideal gas undergoes cyclic changeas shown. The work done in the process is (taking1 atmosphere = 106 dyne/cm2) :
a) 100 J b) 300 Jc) 700 J d) 900 J
8. Specific heat at constant pressure Cp for a
diatomic gas at N.T.P. in the units of cal mole kis :a) 4·95 b) 6·93c) 8·93 d) l.
9. Let a small block of ice of 0°C fall from a certain
height into a water k. It at 0°C, we find that 1
8th
of molts when it reaches the ground. The heightof the fall is :a) 2100 m b) 4200 mc) 100 m d) 1000 m
10. The amount of heat required to convert 1 gm ofice at – 10°C to steam at 100°C is :a) 725 cal b) 1000 calc) 800 cal d) 80 cal
11. A moving s.nowball is completely melted by itsimpact against a wall. The speed (in ms–1) ofsnow ball is :a) 8·2 × 102 m / b) 2·1 × 102 m / secc) 16·4 × 102 m / s d) none of these.
12. The velocity with which a ball of ice be thrownagainst a wall so that it melts completely is :
a) 2JL b) 2 JL
c) = 2JL d) JL.
13. A moving snowball is completely melted by itsImpact against a wall. The speed (in ms–1) ofsnow ball is :a) 8·2 × 102 m / b) 2·1 × 102 m / secc) 16·4 × 102 m / s d) none of these.
14. From what height a piece of ice at zero degreefall in order that it may melt on reaching theground, assuming no loss of energy on the way
(J = 4·2 J / cal) :a) 3·4 × 106 cm b) 3·4 × 105 cmc) 3·4 × 106 m/s d) 3·4 × 105 cm
15. A bullet moving with velocity v stops suddenlyafter hitting the target and whole of its mass mmelts. If s is the specific heat, L the latent heatand its initial temp. is 25°C and melting point. is475°C, then the velocity v is given by :
a) mL = ms (475 – 25) + 1
2 mv2 / J
b) ms (475 – 25) + mL = 1
2 mv2 / J
c) ms (475– 25) + mL = 2 J / mv2
d) None of the above.16. Two identical samples of a gas are allowed to
expand:(i) isothermally and(ii) adiabatically, the amount of work done is :a) equal in both, the casesb) more for adiabatic expansionc) more for isothermal expansiond) no work is done.
17. The normal temp. of human body is 98·6° F. Whatis the corresponding temp. of human body inCelsius scale:a) 36°C b) 37°Cc) 38°C d) 39°C.
18. A gas at N.T.P. is suddenly compressed to onefourth of its original volume. If y is supposed tobe 3/2 then final pressure is:
a) 4 atmospheres b) 3
2 atmospheres
c) 8 atmospheres d) 1/4 atmospheres.19. A bar made of iron for which = 11 × 10–6 °C–1
is 10.000 cm at 20°C. At 19°C the length is :a) 11 × 10–6 cm longerb) 11 × 10–6 cm shorterc) 11 × 10–5 cm shorterd) 11 × 10–4 cm shorter.
20. The temp. at which centigrade and fahrenheitscales have same reading is :a) – 40°C b) 40°F.c) – 32°F d) 0°C.
21. Cooking food in a pressure cooker saves timeand fuel because:
a) under increased pressure, water can be madeto boil at as temperature higher than 100°Cb) heat losses are reduced to a minimumc) condensation of steam is preventedd) under increased pressure, water can be madeto boil at a temperature much lower than 100°C.
22. Nitrogen is a diatomic gas. Its molar specific heata constant volume is very nearly:
a) 5R
2b)
7R
2
c) 3R
2
d) a) and b) c) depending on the temperature.23. At what temperature will oxygen molecules have
the same root mean square speed as hydrogenmolecules at 300K ?a) 4800 K b) 3600 Kc) 2400 K d) 300 K.
24. During an adiabatic compression of 2 moles of agas, 100 J of work was done. The change in theinternal energy will be:a) 50 J b) – 100 Jc) – 50 J d) 100 J.
25. In a thermodynamic process, a system absorbs 2kilo calorie of heat and at the same time does500 J of work. What is the change in internalenergy of the system:a) – 500 J b) 500 Jc) 7900 J d) 8900 J.
26. Steam at 100°C is passed into 1·1 kg of watercontained in a calorimeter of water equivalent0·02 kg at 15°C till the temperature of thecalorimeter rises to 80°C. The mass of steamcondensed in kilogram is :a) 1·3 kg b) 0·260c) 0·13 kg d) 1/3 kg.
27. A metal ball immersed in alcohol weights W1 at
0°C and W2 at 59°C. The coefficient of cubic
expansion of metal is less than that of alcohol. Ifthe density of the metal is large compared to thatof alcohol then:a) W
1 = W
2b) W
1 > W
2
c) W1 < W
2d) W
2 = 1W
2
28. Two cylinders A and B fitted with pistons containequal amounts of an ideal diatomic gas at 300 K.
The piston of A is free to move, while that of B isheld fixed. The same amount of heat is given tothe gas in each cylinder. If the rise in temperatureof the gas in A is 30 K, then the rise in temperatureof the gas in B is :a) 18 K b) 30 Kc) 42 K d) 50 K.
29. At room temperature (27°C) the r.m.s speed ofthe molecules of a certain diatomic gas is foundto be 1920 ms–1. The gas is:a) O
2b) H
2
c) F2
d) Cl2
30. The average translational energy and the r.m.s.speed of molecules of a sample of oxygen gas at300K are 6·21 × 10–21 J and 484 ms–1 respectively.The corresponding values at 600 K are nearly(assuming ideal gas behaviour) :a) 8·78 × 10–21 J, 684 ms–1
b) 6·21 × 10–21 J, 968 ms–1
c) 12·42 × 10–21 J, 684 ms–1
d) 12·42 × 10–21 J, 968 ms–1
31. In a given process on an ideal gas dW = 0 and
dQ 0. Then for the gas:a) the volume will increaseb) the temperature will increasec) the pressure will remain constantd) the temperature will decrease.
32. For a given mass of a gas in an adiabatic changethe temperature and pressure are relatedaccording to the law:
a) P
T = constant b) PTY = constant
c) P1 – YTY = constant d) PY T1–Y = constant.33. For increasing the efficiency of Carnot's
engine,which of the following is most effective:a) increasing the temperature of source by 80°Cb) decreasing temperature of sink by 80°Cc) increasing temperature of source by 40°C anddecreasing temperature of sink by 40°Cd) all the above steps are equally effective.
34. When an ideal diatomic gas is heated at constantpressure, the fraction of the heat energy suppliedwhich increases the internal energy of gas is :
a) 5
7b)
3
7
d) 3
5d)
2
5
35. The temperature of Helium gas is raised by 10°Cat constant volume. Heat supplied to gas may betaken partly as translational and partly as rotationalkinetic energies. Their respective shares are:a) 60%, 40% b) 100%, 0%c) 0%, 100% d) 50%, 50%.
36. The pressure and density of gas 7
5
changes adiabatically from (P, ) to (P', '). If
' = 32 , then find the ratio of
P '
P :
a) 128 b) 32
c) 1
128d)
1
32
37. The number of dead centres per cycle for a steamengine is:a) 1 b) 2d) 3 d) 4
38. A faulty thermometer has its fixed points marked5°C and 95°C. The thermometer reads thetemperature of body as 59°C. The correcttemperature on Celsius scale is:a) 59°C b) 60°Cc) 45°C d) 58°C.
39. An ideal heat engine is working betweentemperature T
1 adn T
2 has efficiency . If both
the temperatures are raised by 100o k each, thenew efficiency will be :
a) b) less than
c) more than d) cannot be perdicted.
40. The molar specific heat of oxygen at constantpressure, C
P = 7.03 cal/mol °C and R = 8.31
Joules/mol oC. The amount of heat taken by5 moles of oxygen when heated at constantvolume from 10°C to 20°C will be approximately:a) 25 cal b) 250 calc) 50 cal d) 500 cal.
41. Equal volumes of copper and mercury have thesame thermal capacity. Sp. heat of mercury is0.046 cal/gm/oC and density is 13.6 g/c.c. Whatis the density of copper if its specific heat is0.090 ?a) 0.695 g/cc b) 6.95 g/ccc) 13.9 g/cc d) None of these.
their specific heats are 0.12 and 0.09 respectively.What is the ratio of their thermal capacities perunit volume ?a) 8 : 9 b) 9 : 8c) 4 : 3 d) 3 : 4.
43. 70 Calories of heat are required to raise thetemperature of 2 moles at constant pressure from30°C to 35°C, what is the amount of heat requiredin calories to raise the same amount through samerange at contant volume?
( = 1.4)
a) 70 b) 60c) 50 d) 35.
44. Boiling water is changing into steam, under thiscondition the specific heat of water in cals/g/°Cis :a) 1 b) zeroc) d) < 1.
45. What amount of heat is needed to raise thetemperature of 2 × 10–2 kg of nitrogen at roomtemperature to raise its temperature by 45°C atconstant pressure ? (Given molecular mass = 28and R= 8.3 J mol–1 K–1; C
p =712 R):
a) 9.33 cal. b) 93.3 Jc) 933.4 J d) 933.3 cal.
46. Total heat required to convert 50 kg of water at10°C to steam at 100°C (L.H = 2.25 × 106 Jkg–1) :a) 3.13 × 106 cal b) 31.3 × 106 calc) 313 kcal d) 31.3 kcal.
47. For a certain gas the ratio of specific heat is 1.5,for this gas :
a) Cp =
5R
Jb) C
v =
3R
J
c) Cv =
5R
Jd) C
p =
3R
J
48. 22g of CO2 at 27°C is mixed with 16g of O
2 at
37°C. The temperature of mixture is :a) 27°C b) 30.5°Cc) 32°C d) 37°C.
49. For an adiabatic change the value of dP
p is equal
to p
v
CdV change in vol.,
C
:
a) 1/ 2 dV
.V
b) –dV
V
c) dV
.V
d) 2 dV
V
50. A system changes from the state (P1,V
1) to
(P2, V
2) as shown, work done by the system is :
a) 7.5 × 105 J b) 7.5 × 105 ergsc) 12 × 105 J d) 6 × 105 J.
51. A metal ring of mass 2.1 kg and of 10 cm radius
is revolving about its axis 350
11 r.p.s. If the is
dropped in a viscous liquid, then the heatgenerated is (J = 4.2 J/cal) :a) 100 cal b) 1000 calc) 2100 cal d) 50 cal.
52. A 50 g lead bullet (sp. heat = 0.02) is at 30°C. Itis fired vertically upwards with a speed of840 m s–1. On returning to the starting level itstrikes the ice cake at 0°C. Row much ice ismelted ? (L.R. of ice = 80 cal/gm):a) 52.875 g b) 5.2875 gc) 528.75 g d) None of these.
53. A given mass of a gas expands from the state Ato the state B by three paths 1, 2 and 3 as shownin the figure. If W
1, W
2 and W
3 respectively be
the work done by the gas along the three pathsthen
55. Which of the following is not a state function?a) temperature b) pressurec) entropy d) work
56. In an adiabatic change, the pressure andtemperature of a monoatomic gas are relatedas P YY–c, where c equals:
a) 2
5b)
5
2
c) 3
5d)
5
3
57. The efficiency of a Carnot engine is 50% andtemperature of sink is 500 K. If temperature ofsource is kept constant and its efficiency raisedto 60%, then the required temp. of sink will be :a) 100 K b) 600 Kc) 400 K d) 500 K
58. If AB is an isothermal, BC is an isochoric andAC is an adiabatic, which of the graph correctlyrepresents them in Fig. ?
59. Which of the following PV diagrams bestrepresents an isothermal process :
a) A b) Cc) B d) D
60. The volume of a metal sphere increases by 0·24%when its temperature is raised by 40°C. Thecoefficient of linear expansion of the metal is.....°C–1 :a) 2 × 10–5 b) 18 × 10–5
c) 6 × 10–5 d) 1·2 × 10–5
61. Which statement is incorrect?a) All reversible cycles have same efficiencyb) Reversible cycle has more efficiency than anirreversible onec) Carnot cycle is a reversible cycled) Carnot cycle has the maximum efficiency inall cycles.
62. Even Carnot engine cannot give 100% efficiencybecause we cannot:a) prevent radiationb) find ideal sourcesc) reach absolute zero temperature for sinkd) eliminate friction.
63. Heat given to a body which raises its temperatureby 1°C isa) water equivalent b) thermal capacityc) specific heat d) temperature gradient
64. Which of the following is incorrect regarding thefirst law of thermodynamics?a) It introduces the concept of the entropyb) It introduces the concept of internal energyc) It is a restatement of the principle ofconservation of energyd) It is not applicable to any cyclic process
65. A system goes from A to B via two processes I
and II as shown in Fig. If 1U and 2U are the
changes in internal energies in the processes Iand II respectively, then:
at constant temperture T, the correct plot of P.Vdiagram for it is :
67. An ideal gas confined to an insulated chamber isallowed to enter into an evacuated insulated
chamber. If Q.W and intE have the usual
meanings, thena) Q = 0, W 0 b) W = 0, Q 0
c) intE = 0, Q 0 d) Q = W = intE = 0.
68. The internal energy of one gram of helium at100 K and one atmospheric pressure is :a) 100 J b) 1200 Jc) 300 J d) 500 J
LEVEL – II
69. The P–V diagram for a cyclic process is a triangleABC drawn in order. The co–ordinates of A, B,C are (4,1), (2,4) & (2,1). The co–ordinates arein order of P – V in which P is in N / m2 & volumein litres. The work done during the process fromA to B is :a) 3 × 10–3 J b) –3 × 10–3 Jc) 6 × 10–3 J d) 9 × 10–3 J.
70. In Q.No. 69, work done in complete cycle is :a) 3 × 10–3 J b) –3 × 10–3 Jc) 6 × 10–3 J d) zero
71. The density of a liquid of coefficient of cubicalexpansion is d at 0°C. When the liquid is heatedto a temperature T, the change in density willbe :
a) 0Td
(1 T)
b)
0Td
(1 T)
c) 0(1 T)d
T
d)
0(1 T)d
T
72. Two blocks of ice join together where pressed.Which one of the following will appropriatelyaccount for this ?a) The melting point of ice decreases withincrease in pressureb) The melting point of ice increases withincrease in pressurec) The latent heat of fusion of ice is highd) Ice blocks have a; natural affinity for eachother.
73. The equation of state for a real gas such ashydrogen oxygen etc. is called the Van der waal's
equation which reads: 2
aP
V
(V – b) – = n
RT where a and b are constants of the gas. Thedimensional formula of constant a is :a) M–1L5T–1 b) ML5T–2
c) ML–1T–1 d) None of these.74. An ideal gas is initially at temperature T and
76. For a monoatomic gas in adiabatic process, therelation between the pressure and absolutetemperature time T is P TC where C equalto :
a) 2
5b)
3
5
c) 5
2d)
1
3
77. If the degrees of freedom of a gas are f, then the
ratio of its specific heats P
v
C
C is given by:
a) 1 – 2
fb) 1 +
2
f
c) 1 + 1
fd) 1 –
1
f
78. A volume V and temperature T was obtained, asshown in diagram, when a given mass of gas washeated. During the heating process the pressureis :
a) increased b) decreasedc) remains constant d) changed erratically.
79. A vessel containing air of mass 8g at 400 K is
provided with a hole so that some amount of airleaks out. After some time, the pressure is halvedand temperature is changed to 300 K. The massof air escaped is :a) 4 g b) 2.7 gc) 5.3 g d) 2 g.
80. If one mole of a monoatomic gas = 5
3, is mixed
with one mole of diatomic gas 7
5 what is the
value of for the mixture ?
a) 3
2b)
5
2
c) 6
5d)
8
5
81. Pure water cooled to – 15°C is contained in athermally insulated flask. Some ice is added intothe flask. The fraction of water frozen into iceis :
a) 3
35b)
6
35
c) 2
35d)
6
29
82. One mole ofmonoatomic gas is mixed with threemoles of diatomic gas. What is molecular specificheat of the mixture at constant volume?R = 8.31 J/mole/K :a) 18.7 J/mole/K. b) 1.87 J/mole/K.c) 9.35 J/mole/K. d) 4.67 J/mole/K..
83. Half a mole of helium is contained in a containerat S.T.P. How much heat energy is needed todouble the pressure of the gas, keeping the volumeconstant? Heat capacity of the gas is 3J/g/K. :a) 1.638 J b) 16.38 Jc) 163.8 J d) 1638 1.
84. A Camot's engine is working between 7°C and287°C. It is desired to increase its efficiency to70%. By how much should the temperature ofsource be increase ?a) 273°C b) 173°Cc) 373.3°C d) – 273.3°C.
85. When a gas enclosed in a closed vessel washeated so as to increase its temperature by 5°C,its pressure was seen to have increased by 1 %.
The initial temperature of the gas was nearly :a) 500°C b) 273°Cc) 227°C d) 150°C
86. One mole of an ideal gas at an initial temperatureof TK does 6 R joule of work adiabatically. If theratio of specific heats of this gas at constantpressure and at constant volume is 5/3, the fmaltemperature of the gas will be:a) (T + 4) K b) (T + 2·4) Kc) (T – 4) K d) (T–2·4) K
87. The temperature of equal masses of threedifferent liquids A, B and C are 12°C, 19°C and28°C respectively. The temperature when A andB are mixed is 16°C and when B and C are mixedis 23°C. The temperature when A and C aremixed is :a) 18·2 °C b) 20·2°Cc) 22°C d) 24·2°C
88. A Carnot engine whose sink is at 300 K has anefficiency of 40%. By how much should thetemperature of source be increased so as toincrease its efficiency by 50% of originalefficiency:a) 380 K b) 275 Kc) 325 K d) 250 K.
89. A lead bullet of mass 21 g travelling at a speed100 m s–1 comes to rest after striking a woodenblock. The rise in temperature of the bullet is :(Sp. heat of lead = 30 cal/kg°C)a) 25 °C b) 28 °Cc) 33 °C d) 39 °C.
90. The ratio of specific heats for O2 is 1.4. Density
of O2 at N.T.P. is 1.44 kg/m3. If the normal
pressure is 1.01 × 3 × 105 N/m2, the specific heatC
v is:
a) 257.7 J kg–1 K–1 b) 644.3 J kg–1 K–1
c) 8.36 J kg–1 K–l d) 901.2 J kg–1 K–1.91. A vessel contains 100 g of water. The heat
capacity of vessel is equal to 10 g of water. Theinitial temperature of water in vessel is 10oC. If220 g of hot water at 70°C is poured in, the finaltemperature will be :a) 40°C b) 50°Cc) 60°C d) 70°C
92. Adiabatic relation for temperature and volumeis:
a) V.T = constant b) 1V . T = constant
c) V
T = constant d) V .T = constant.
93. The height of a water fall is 100 metres. Thedifference of temperature of the water which fallson an insulator is :a) 0.23°C b) 2.3°Cc) 23°C d) None of these.
94. dU = – dW is true for :a) isothermal process b) adiabatic processc) isobaric process d) isochoric process.
95. The ratio of the slopes of adiabatic to that of anisothermal is :
a) b) – 1
c) 1
d) 1
1
96. The gas is expanded adiabatically and itstemperature falls to T
1. It is then expanded
isothermally and temperature now is T2. Then:
a) T1 > T
2
b) T1 = T
2
c) T1 < T
2
d) T1 is nearly equal to T
2.
97. A monoatomic gas ( = 5/3) is suddenlycompressed to 1/8th of its volume adiabaticallythen the pressure of the gas will change to (timesthe initial pressure) :a) 24/5 b) 8c) 40/3 d) 32.
98. 20 g of a gas occupies 100 cc volume at 105 dyne/cm2 pressure. If during isothermal process thepressure is changed to 104 dyne/ cm2, the volumeof the gas in cc will be :a) 10 b) 50c) 200 d) 1000.
99. For an adiabatic change the value of dP
P is equal
to p
v
CdV change in vol.,
C
a) 1/ 2 dV
.V
b) –dV
V
c) dV
.V
d) 2 dV
V
100. For an isothermal expansion of a perfect gas the
101. An ideal monoatomic gas is taken round the cycleABCDA as shown. The work done during thecycle is:
a) P.V b) 1
2 P.V
c) 2 P.V d) zero.102. A system changes from the state (P
1, V
1) to (P
2,
V2) as shown, work done by the system is :
a) 7.5 × 105 J b) 7.5 × 105 ergc) 12 × 105 J d) 6 × 105 J.
103. The pressure and density of a diatomic gas
7
5
changes adiaba~ically from (P, ) to
(P', '). If '
= 32, then
P '
P is:
a) 1
128b) 128
c) 32 d) None of these.
104. Starting with the same initial conditions, an idealgas expands from volume V
1 to V
2 in three
different ways. The work done by the gas is W1
if the process is purely isothermal, W2 if purely
isobaric and W3 if purely adiabatic. Then
a)W2 > W
1 > W
3b)W
1 > W
2 > W
3
c)W2 > W
3 > W
1d)W
1 > W
3 > W
2
105. A Carnot engine takes 3 × 106 cals of heat froma reservoir at 627°C and gives it to a sink at 27°C.The work done by the engine is :a) 4·2 × 106 J b) 16·8 × 106 Jc) 8·4 × 106 J d) 3 × 106 J
106. An ideal gas expands isothermally from a volumeV
1 to V
2 and then compressed to original volume
V1 adiabatically. Initial pressure is P
1 and final
pressure is P3. Total work done is W. Then which
is true :a) P
3 > P
1 ; W > 0 b) P
3 > P
1 ; W < 0
c) P3 < P
1 ; W < 0 d) P
3 = P
1 ; W = 0
107. Liquid oxygen at 50 K is heated to 300 K atconstant pressure of 1 atm. The rate of heatingis constant. Which of the following graphsrepresents the variation of temperature withtime ?
108. A gaseous mixture consists of 16g of helium and
16 g of oxygen. The ratio p
v
C
C of the mixture is :
a) 1·54 b) 1·62c) 1·4 d) 1·59
109. Water of volume 2 litre in a container is heatedwith a coil of 1 kW at 27°C. The lid of thecontainer is open and energy dissipates at the rateof 160 J/s. In how much time, temperature willrise from 27°C to 77°C ?[Given specific heat of water is 4·2 kJ/kg] :a) 8 min 20 s b) 7 minc) 6 min 2 s d) 14 min
110. Calorie is defmed as the amount of heat requiredto raise temperature of 1 g of water by 1°C andit is defmed under which of the followingconditions?a) From 14·5 °C to 15·5 °C at 760 mm of Hgb) From 98·5 °C to 99·5 °C at 760 mm of Hgc) From 13.5 °C to 14·5°C at 76 mm of Hgd) From 3·5°C to 4·5°C at 76 mm of Hg.
111. A rigid container with thermally insulated walls
contains a coil of resistance 100 , carryingcurrent 1 A. Change in internal energy after5 minute will be :a) 0 kJ b) 20 kJc) 10 kJ d) 30 kJ
112. The work of 146 kJ is performed in order tocompress one kilo mole of a gas adiabatically andin this process the temperature of the gas increasesby 7°C. The gas is (R = 8·3 J mol–1 K–1) :a) diatomicb) triatomicc) a mixture of monoatomic and diatomicd) monoatomic.
113. If Cp and C
v denote the specific heats of nitrogen
per unit mass at constant pressure and constantvolume respectively, then
a) Cp – C
v =
R
14b) C
p – C
v = R
c) Cp – C
v = 28 R d) C
p – C
v =
R
28
114. The speed of sound in oxygen (O2) at a certain
temperature 66 ms–1. The speed of sound inhelium (He) at the same temperature will beassume both gases to be ideal)a) 421 ms–1 b) 500 ms–1
c) 650 ms–1 d) 300 ms–1
115. Dry air ( = 1.5) at atmospheric pressure is
suddenly compressed to 1
4th of its original
volume, the pressure will be :a) 10 atmosphere b) 8 atmospherec) 3 atmosphere d) 6 atmosphere.
116. Cp and C
v denote the molar specific heat
capacities of a gas at constant volume andconstant pressure, respectively. Thena) C
p – C
v a larger to a diatomic ideal gas than
for a monoatomic ideal gas.
b) Cp + C
v is larger for a diatomic ideal gas than
for a monoatomic ideal gas.c) C
p /C
v is larger for a diatomic ideal gas than
for a monoatomic ideal gas.d) C
p – C
v is larger for a diatomic ideal gas than
for a monotomic ideal gas.117. A diatomic ideal gas is used in a Camot engine as
the working substance. If during the adiabaticexpansion part of the cycle, the volume of thegas increases from V to 32 V, the efficiency ofthe engine is :a) 0.25 b) 0.5c) 0.75 d) 0.99.
118. A piece of ice (heat capacity = 2100 J kg–1 °C–1
and latent heat = 3.36 × 105 J kg–1) of mass mgrams is at –5°C at atmospheric pressure. It isgiven 420 J of heat so that the ice starts melting.Finally when the ice–water mixutre is inequilibrium, it is found that 1 gm of ice has melted.Assuming there is no other heat exchange in theprocess, the value of m is .a) 2 b) 4c) 6 d) 8.
119. The isothermal diagram of a gas at three differenttemperatures T
1, T
2 and T
3, is shown in the given
figure. Then
a) T1 < T
2 < T
3b) T
1 < T
2 > T
3
c) T1 > T
2 > T
3d) T
1 > T
2 < T
3
120. One mole of an ideal gas goes from an initial stateA to final state B via two processes : It firstundergoes isothermal expansion from volume Vto 3V and then its volume is reduced from 3V toV at constant pressure. The correct P–V diagramrepresenting the two processes is:
121. Four moles of carbon monoxide are mixed withfour moles of carbon dioxide. Assuming the gasesto be ideal, the ratio of specific heats is :a) 15/11 b) 41/30c) 4/3 d) 7/4.
122. For a monatomic ideal gas undergoing an adiabaticchange, the relation between temperature andvolume is TVx = constant where x is :a) 7/5 b) 2/5c) 2/3 d) 1/3.
123. Read the two statements – (I) When a solid meltsand changes to liquid state, its volume mayincrease or decrease. (II) As a result of increasein pressure, the melting point at a solid may beraised or lowered. With reference to thesestatements, the only correct statements out of thefollowing'sa) (I) is true but (II) cannot be trueb) (I) cannot be true but (II) is truec) (I) and (II) both are true and (I) is the causeof (II)d) (I) and (II) both are true and they areindependent of each other.
Recent competitive Questions :
124. A thermally insulated vessel contains an ideal gasof molecular mass M and ratio of specific heats . It is moving with speed v and it is suddenlybrought to rest. Assuming no heat is lost to thesurroundings, its temperature increases by :
a) 2( 1)
Mv K2 R
b)
2MvK
2R
c) 2( 1)
Mv K2R
d)
2( 1)Mv K
2( 1)R
125. Three perfect gases at absolute temperatures T1,
T2 and T
3 are mixed. The masses of molecules
are m1, m
2 and m
3 and the number of molecules
are n1, n
2 and n
3 respectively. Assuming no less
of energy, the final temperature of the mixtureis :
a) 1 1 2 2 3 3
1 2 3
n T n T n T
n n n
b)
2 2 31 1 2 2 3 3
1 1 2 2 3 3
n T n T n T
n T n T n T
c)
2 2 2 2 3 31 1 2 2 3 3
1 1 2 2 3 3
n T n T n T
n T n T n T
d) 1 2 3(T T T )
3
126. A Carnot engine operating between temperatures
T1 and T
2 has efficiency
1
6. When T
2 is lowered
by 62 K its efficiency increases to 1
3. Then T
1
and T2 are, resectively :
a) 372 K and 330 K b) 330 K and 268 Kc) 310 K and 248 K d) 372 K and 310 K
127. 100 g of water is heated from 30° to 50° C.Ignoring the slight expansion of the water, thechange in its internal energy is (specific heat ofwater is 4184 J/kg/K) :a) 8.4 kJ b) 84 kJc) 2.1 kJ d) 4.2 kJ
128. The specific heat capacity of a metal at lowtemperature (T) is given as :
Cp(kJK–1k–1) = 32
3T
400
A 100 gram vessel of this metal is to be cooledfrom 20K to 4K by a special refrigerator operatingat room temperature (27°C). The amount of workrequired to cool the vessel is :a) greater than 0.148 kJb) between 0.148 kJ and 0.028 kJc) less than 0.028 kJd) equal to 0.002 kJ
129. A metal rod of Young's modulus Y and coefficientof thermal expansion a is held at its two endssuch that its length remains invariant. If itstemperature is raised by toC, the linear stressdeveloped in it is :
a) Y
tb) Y t
c) 1
(Y t) d) t
Y
130. An aluminium sphere of 20 cm diameter is heatedfrom oC to 100 °C. Its volume changes by (giventhat coefficient of linear expansion for aluminium Al
131. 5.6 litre of helium gas at STP is adiabaticallycompressed to 0.7 litre. Taking the initialtemperature to be T
1, the work done in the
process is
a) 9
8RTT
1b)
3
2RTT
1
c) 15
8RTT
1d)
9
2RTT
1
132. Steel wire of length 'L' at 40° C is suspendedfrom the ceiling and then a mass 'm' is hung fromits free end. The wire is cooled down from 40°Cto 30°C to regain its original length 'L'. Thecoefficient of linear thermal expansion of the steelis 10–5/oC, Young's modulus of steel is 1011N/m2
and radius of the wire is 1 mm. Assume thatL >> diameter of the wire. Then the value of 'm'in kg is nearlya) 1 b) 2c) 3 d) 4
133. Helium gas goes through a cycle ABCDA(consisting of two isochoric and two isobaric lines)as shown in figure. Efficiency of this cycle isnearly:(Assume the gas to be close to ideal gas)a) 12.5% b) 15.4%c) 9.1% d) 10.5%.
134. A Carnot engine, whose efficiency is 40%, takesin heat from a source maintained at atemperature of 500 K. It is desired to have anengine of efficiency 60%. Then, the intaketemperature for the same exhaust (sink)temperature must be :a) 600 Kb) efficiency of Carnot engine cannot be madelarger than 50%c) 1200 Kd) 750 K.
135. A wooden wheel of radius R is made of twosemicircular parts (see figure). The two parts areheld together by a ring made of a metal strip ofcross sectional area S and length L. L is slightlyless than 2 R. To fit the ring on the wheel, it isheated so that its temperature rises by T and itjust steps over the wheel. As it cools down tosurrounding temperature, it presses the
semicircular parts together. If the coefficient oflinear expansion of the metal is , and its Youngsmodulus is Y, the force that one part of the wheelapplies on the other part is :
a) 2SY T b) 2 S Y T
c) SY T d) SY T..
136.
The above p–v diagram represents thethermodynamic cycle of an engine, operating withan ideal monoatomic gas. The amount of heatextracted from the source in a single cycle is :
a) 13
2
P0 YY
0b)
11
2
P0Y
0
c) 4P0Y
0d) P
0Y
0
137. One mole of diatomic ideal gas undergoes a cyclicprocess ABC as shown in figure. The processBC is adiabatic. The temperature at A, B and Care 400 K, 800 K and 600 K respectively. Choosethe correct statement:
a) The change in internal energy in the processBC is –500R.b) The change in internal energy in whole cyclicprocess is 250 R.c) The change in internal energy in the processCA is 700Rd) The change in internal energy in the processAB is – 350 R.
138. The pressure that has to be applied to the ends ofa steel wire of length 10 cm to keep its lengthconstant when its temperature is raised by 100°Cis :
(For steel Young's modulus is 2 × 1011N m–2 andcoefficient of thermal expansion is 1.1 × 10–5 K–1)a) 2.2 × 106 Pa b) 2.2 × 108 Pac) 2.2 × 109 Pa d) 2.2 × 107 Pa.
139. A solid of constant heat c.ipacity 1 J/oC is beingheated by keeping it in contact with reservoirs intwo ways:(i) Sequentially keeping in contact with 2reservoirs such that each reservoir supplies sameamount of heat.(ii) Sequentially keeping in contact with 8reservoirs such that each reservoir supplies sameamount of heat.In both the cases body is brought from initialtemperature 100°C to final temperature 200°C.Entropy change of the body in the two casesrespectively is :a) ln2, ln2 b) ln2, 2ln2c) 2ln2, 8ln2 d) ln2, 4ln2.
140. Consider an ideal gas confined in an isolatedclosed chamber. As the gas undergoes anadiabatic expansion, the average time of collisionbetween molecules increases as Vq, where Y isthe volume of gas. The value of q is :
p
V
C
C
a) 3 5
6
b)
1
2
c) 1
2
d)
3 5
6
141. Figure below shows two paths that may be takenby a gas to go from a state A to a state C.
In process AB, 400 J of heat is added to thesystem and in process BC, 100 J of heat is addedto the system. The heat absorbed by the systemin the process AC will be :a) 380 J b) 500 J
c) 460 J d) 300 J.
142. A Carnot engine, having an efficiency of =
1
10 as heat engine, is used as a refrigerator. If
the work done on the system is 10 J, the amountof energy absorbed from the reservoir at lowertemperature is :a) 100 J b) 99 Jc) 90 J d) 1 J.
143. One mole of an ideal diatomic gas undergoes atransition from A to B along a path AB as shownin the figure,
The change in internal energy of the gas duringthe transition is :a) 20 kJ b) – 20 Jc) 20 kJ d) –12 kJ.
144. The ratio of the specific heats P
V
C
C in terms
of degrees of freedom (n) is given by :
a) 1
1n
b) n
13
c) 2
1n
d) n
12
145. Gases exert pressure on the walls of the containerbecause the gas molecules :a) Have finite volumeb) Obey Boyle's lawc) Possess momentumd) Collide with one another.
146. A hollow sphere of mass 'M' and radius 'R' isrotating with angular frequency ' ', It suddenlystops rotating and 75% of kinetic energy isconverted to heat. If 'S' is the specific heat of thematerial in J/kg K then rise in temperature of the
