Physics 20: Heat Teacher Notes Page 1 of 24 Kinetic Molecular Theory A theory is a collection of ideas that attempts to explain certain phenomena. A law is a statement of specific relationships or conditions in nature. After centuries of questioning and puzzling over the nature of heat, scientists now believe that heat is linked to the way molecules move - the Kinetic Molecular Theory. This theory is helpful in describing temperature, heat, and thermal energy. Some of the key features of this theory are listed below. All matter is made of atoms, which may combine to form molecules. Atoms and molecules are in a constant, random, state of motion. Molecular motion is greatest in gases, less in liquids, and least in solids. Molecules in motion have kinetic energy. Molecules separated from one another have electric potential energy. Collisions between moving molecules transfer energy between them.
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Physics 20: Heat Teacher Notes
Page 1 of 24
Kinetic Molecular Theory
A theory is a collection of ideas that attempts to explain certain
phenomena.
A law is a statement of specific relationships or conditions in nature.
After centuries of questioning and puzzling over the nature of heat,
scientists now believe that heat is linked to the way molecules move -
the Kinetic Molecular Theory. This theory is helpful in describing
temperature, heat, and thermal energy.
Some of the key features of this theory are listed below.
All matter is made of atoms, which may combine to form
molecules.
Atoms and molecules are in a constant, random, state of motion.
Molecular motion is greatest in gases, less in liquids, and least in
solids.
Molecules in motion have kinetic energy.
Molecules separated from one another have electric potential
energy.
Collisions between moving molecules transfer energy between
them.
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Solids
Attractive electrical forces cause molecules to vibrate but stay in a
fixed position. Solids maintain their shape and volume.
Liquids
Attractive force is weaker in a liquid - - molecules are further apart
and move about quickly. Liquids maintain their volume but not their
shape.
Gases
Attractive force is very weak in a gas - - molecules are far apart and
move about very quickly. Gases do not maintain their shape or volume.
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Thermal Energy
Molecules have two forms of energy - - kinetic because of their motion,
and potential because of the electric forces holding them together.
Thermal energy is the total of all kinetic and potential energies, or the
total energy of all particles in a substance.
Figure 1
The happy face molecules move around a lot and have lots of kinetic
energy. The sad face molecules are sleepy and have little kinetic but
lots of potential energy. The thermal energy above is the sum of the
happy and sleepy molecules.
Figure 2
There are more happy face molecules and sleepy face molecules in
Figure 2. Therefore the thermal energy is much greater than in Figure
1 because thermal energy is the sum of all energies.
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Transferring Thermal Energy
Heat is the thermal energy transferred from one object to another
due to differences in temperature. Heat (thermal energy) can be
transferred by conduction, convection, and radiation.
Conduction
Particles gain energy from the flame.
They vibrate faster, and as they collide with other particles
energy is passed from particle to particle.
Convection (Currents)
Particles gain energy near heater.
Warm air above is less dense and easier for heated air particles
to rise.
As warm air is rising, cool air from the side replaces heated air
causing a circular convection current.
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Radiation
Radiation is the transfer of energy by electromagnetic waves.
Heat radiation is the infrared portion of the electromagnetic
spectrum.
Thermal energy from the sun can travel through a vacuum at the
speed of light, so no particles are needed as in conduction or
convection.
The best surfaces for transmitting or absorbing radiant heat are
black, rough surfaces. Car radiators and cooling coils on the back
of fridges are painted black to exchange heat quickly.
The best surfaces for reflecting (not absorbing) radiant heat are
smooth and white surfaces. That's why you stay cooler in the
summer with white clothes and thermos bottles are shiny on the
inside surface.
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Temperature
Recall that thermal energy was the total of all energies in a substance.
Temperature is a measure of the average energy of the particles that
make up a substance.
Figure 1
Figure 2
The thermal energy of Figure 2 is twice as much as Figure 1 (double
the particles). However, the temperature of Figure 1 and 2 is the same
because temperature is the average of the energies in the substance.
Temperature can be measured with a thermometer.
Thermometers
Most thermometers are based on the property that materials
expand when heated and contract when cooled. For example, in liquid
thermometers, alcohol or mercury expand when heated and rise up a
glass tube. A scale on the glass tube allows us to read the temperature.
Thermometers must be calibrated. One way to calibrate is by
analyzing the amount of thermal expansion and contraction that occurs
within a given type of substance.
Thermometers are ________ by the physical properties of the
substance from which they are made. (i.e. An alcohol thermometer
can’t be used above the boiling point of alcohol, and a mercury
thermometer can’t be used below the freezing point of mercury.)
Temperature Scales
The Celsius scale is commonly used to measure temperature. Its scale
has been calibrated to the physical properties of pure water. The
normal freezing point of water was arbitrarily set as 0 oC and the
normal boiling point of water was arbitrarily set at 100 oC.
The Kelvin scale, also called the Absolute scale, sets 0 K as absolute
zero (-273.15 oC). Temperature increases on the scale are the same as
on the Celsius scale (1 K = 1 oC).
Converting Celsius to Kelvin
Use: K = C + 273 Example: Convert 25°C to K K = 25 + 273 = 298K
Converting Celsius to Fahrenheit (not used much)
Use F = 9/5C +32 Example: Convert 20°C to °F F = 9/5C +32 = 68°F
Converting Kelvin to Celsius
Use: C = K - 273 Example: Convert 393K to C° C = 393 - 273 = 20°C
Converting Fahrenheit to Celsius (not used much)
Use C = 5/9(F-32) Example: Convert 80°F to °C C = 5/9(F-32) = 26.7°C
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Practice Problems K = C + 273 C = K – 273 1. Convert these temperatures from Celsius to Kelvin:
a) 27C = 300 K
b) 560C = 833 K
c) -184C = 89 K
d) -273C= 0 K 2. Convert Kelvin to Celsius:
e) 110K = -63C
f) 22K = -251C
g) 402K = 129C
h) 323K = 50C
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Thermal Expansion
We already know that thermal expansion provides a method of
measuring temperature. At the level of atoms and molecules, thermal
expansion occurs because the distance between molecules increases
as their thermal energy increases.
1. Linear Expansion
Solids expand in all directions (length, width, thickness) when heated,
and similarly contract when cooled.
For long, thin objects the change is most noticeable only in length. The
change in length in one direction is termed linear expansion.
Linear expansion depends on several factors: change in temperature,
original length, type of material.
Where: is the change in length (m)
is the coefficient of linear expansion (°C)
is the original length (m)
is the temperature change (°C)
The coefficient of linear expansion is different for different
materials. The thermal expansion of materials must be considered in
the design of certain kinds of structures.
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2. Volume Expansion
Just as linear expansion occurs in solids, volume expansion occurs in
liquids and gases. Volume expansion depends on the change in
temperature, original volume, and the type of substance.
Volume expansion is extremely important in gases. (It is extremely
important to recognize any potentially hazardous situations which could
result in an increase in pressure in closed containers.)
Where: is the change in volume (m3)
is the coefficient of volume expansion (°C-1)
is the original volume (m3)
is the temperature change (°C)
Coefficients of Thermal Expansion
SUBSTANCE COEFFICIENT OF LINEAR EXPANSION
(X10-6 C -1)
COEFFICIENT OF VOLUME EXPANSION
(X10-6 C -1)
Aluminum 24
Brass 19
Concrete 10-14
Copper 17
Glass (window) 9.0
Glass (Pyrex) 3.3
Granite 8.3
Ice 50
Lead 27
Steel or iron 12
Ethyl alcohol 1100
Gasoline 950
Mercury 182
Water 210
Antifreeze 108
Air & most gases 3400
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Expansion Example Problems
1. A steel bridge in Saskatoon is 380 m long. If the temperature varies
from -40.0 °C to 30.0 °C, what is the change in the length of the
bridge for this temperature range?
Note
2. A gasoline tank in a truck holds 60.0 litres at 20°C. If the tank is
filled to the top and the daytime temperature goes up to 45°C, how
much gas will overflow?
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Expansion Practice Problems
1. A brass rod is .500 m long at 20.0C. What is the length of the rod if it is heated to
50.0C?
2. A steel beam 12.0m sits next to a concrete wall when the temperature is 20.0C. A gap must be left between the beam and the concrete wall for expansion purposes. If the
temperature rises to 45.0C, how large must the gap be if the steel beam just touches the concrete wall?
3. There are 500 m3 of air in a shop at 20.C. What is the difference in volume if the
temperature is 0C?
4. A metal rod .50 m is heated from 15C to 95C. The length of the rod increases by 0.96 mm. What is the coefficient of expansion for the rod?
Answers
1. 2.85 x 10-4 m 2. 3.60 x 10-3 m 3. 34 m3 4. 2.4 x 10-5 ºC-1
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The Abnormal Behaviour of Water
Most liquids expand as the temperature increases. But not water!
From 0oC to 4oC water contracts as heated. (Above 4oC, water
behaves normally.)
Notice above that the volume of water starts to expand when less than 4°C. Therefore, water has the greatest density at 4°C, not at 0°C.
Water expands when it freezes. The expansion results in a decrease
in density, allowing ice to float on water.
Water also has a high specific heat capacity compared to other
liquids.
Without this cool characteristic of water, no fish could survive in lakes
in winter!
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Specific Heat Capacity
Recall:
Heat is the energy that flows from one object to another due to
a difference in their temperatures.
When heat flows into an object its thermal energy increases, as
does its temperature.
The quantity of heat energy (thermal energy) in a substance
depends on its temperature, mass, and type of substance
(specific heat capacity).
Specific heat capacity is the quantity of heat (energy) needed to
raise the temperature of 1 kg of a substance by 1°C. Heat, like other
energies, is measured in the unit, joules (J).
Temperature can be measured using a thermometer. However, heat
must be calculated using the formula:
where: Q is the quantity of heat gained or lost (J)
m is the mass (kg)
c is the specific heat capacity (J/kg•°C)
ΔT is the temperature change (°C)
Substances with a low specific heat capacity warm quickly because
they need less heat energy for a given change in temperature. They
also give up their heat quickly.
Substances with a high specific heat capacity take a long time to warm
up and they retain their heat for a long time.
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Specific Heat Capacity Values
Substance Specific Heat
Capacity J/kg°C Substance
Specific Heat Capacity J/kg°C
aluminum 9.0 x 102 alcohol (ethyl) 2.3 x 102
brass 3.8 x 102 alcohol (methyl) 2.5 x 102
copper 3.9 x 102 glycerine 2.4 x 102
glass (crown) 6.7 x 102 mercury 1.4 x 102
glass (pyrex) 7.8 x 102 nitrogen (liquid) 1.1 x 102
gold 1.3 x 102 water (liquid) 4.2 x 103
iron 4.5 x 102 water (ice) 2.1 x 103
lead 1.3 x 102 water (steam) 2.0 x 103
sand 8.0 x 102 air 1.0 x 103
silver 2.3 x 102
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Specific Heat Example Problems
1. How much heat is needed to raise the temperature of 2.0 kg of
copper from 20.0°C to 70.0°C?
Note: For most temperature changes, use the absolute value to simplify the
mathematics. Treat specific heat capacity (c) as a constant - do not use for
determining significant digits.
2. A 1.0 kg aluminum block has an initial temperature of 10.0°C. What
will the final temperature of the aluminum block be if 3.0 x 104 J of
heat is added?
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Specific Heat Practice Problems
1. When 3.0 kg of water is cooled from 80.0C to 10.0C, how much heat energy is lost?
2. How much heat is needed to raise a 0.30 kg piece of aluminum from 30.C to 150C?
3. Calculate the temperature change when:
a) 10.0 kg of water loses 232 kJ of heat.
b) 1.96 kJ of heat are added to 500. g of copper.
4. 2.52 x 104 J of heat are added to 2.0 kg of mercury to reach a final temperature of
130C. What was the initial temperature of the mercury? Answers 1. 8.8 x 105 J 2. 3.2 x 104 J 3 a) 5.52 ºC b) 10.1 ºC 4. 40ºC
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Latent Heat & Change of State
Adding or removing heat does not always result in a change of
temperature. During a change of state, the heat added is called
latent heat because there is no change in temperature. Latent means
"hidden".
Notice in the graph above that while ice is melting (change of state)
the temperature stays constant at 0°C. The temperature also is
constant when water boils and changes to steam or vapour.
When a solid is melting the heat energy added is building up the
potential energy of the molecules to break the electrical forces holding
them together. Similarly, when liquids are turning to gases the heat
energy increases the energy of the molecules so they get further
apart and become gas molecules.
Latent heat of fusion is the amount of heat required to melt 1 kg of a
substance without changing its temperature. The latent heat of fusion
for water is 3.3 x 105 J/kg, which means that 3.3 x 105 J of energy are
needed to change 1 kg of ice at 0°C into water at 0°C.
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Latent heat of vaporization is the amount of heat required to
vaporize 1 kg of a substance without changing its temperature.
Latent Heat Formula:
where: QL is the quantity of heat (J)
m is the mass (kg)
is the latent heat of the substance (J/kg)
Latent Heat Values
Substance Heat of Fusion
(J/kg) Heat of Vaporization
(J/kg)
water 3.3 x 105 2.3 x 106
alcohol (ethyl) 1.4 x 104 8.5 x 105
alcohol (methyl) 6.8 x 104 1.1 x 105
gold 6.3 x 104 1.6 x 105
lead 2.5 x 104 8.7 x 105
mercury 1.2 x 104 2.7 x 105
silver 8.8 x 104 2.4 x 106
nitrogen 2.5 x 104 2.0 x 105
oxygen 1.4 x 104 2.1 x 105
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Latent Heat Example Problems
1. How much heat energy is needed to change 2.0 kg of ice at 0°C to water at 0°C?
2. How much heat energy is needed to change 0.50 kg of water at 100°C to steam
at 100°C?
3. How much heat does a refrigerator need to remove from 1.5 kg of water at 20.0
°C to make ice at 0°C?
[Hint: Find heat removed for water at 20.0°C to water at 0°C, then find latent
heat for water at 0°C to ice at 0°C, and add the two values.]
The above example can also be done by combining latent heat and heat with
temperature change into 1 long equation.
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Latent Heat Practice Problems
1. How much heat must be added to a 25g ice cube at 0ºC to change it to water at 0ºC?
2. How much heat is lost when 0.10kg of steam at 100.ºC condenses to water at 80. ºC?
3. How much heat is needed to change 0.10kg of ice at –20.ºC. to steam at 110ºC?
[Hint: for question 3, remember to use the specific heat capacity value for steam and ice, which
is different from liquid water.]
Answers 1. 8.3 x 103 J 2. 2.4 x 105 J 3. 3.1 x 105 J
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Thermodynamics
Thermodynamics is the field of physics that deals with the relationship
between heat and other forms of energy.
Recall that when there is a transformation of energy between
substances, heat lost = heat gained. In other words, the total amount
of energy stays constant (the Law of Conservation of Energy).
The First Law of Thermodynamics
The quantity of heat energy transferred to a system is equal to the
work done by the system plus the change in the internal energy of the
system.
The Second Law of Thermodynamics
The natural flow of heat is from a hot object to a cold object. In other
words, energy, when converted from one form to another, can only be
lost and not gained.
The Third Law of Thermodynamics
Absolute zero can never be reached. Absolute zero is the temperature
at which all molecular movement stops.
Principle of Heat Exchange
Whenever two substances at different temperatures are allowed to mix, heat travels from the hotter substance to the colder one. The quantity of heat given off by the hotter substance is equal to the quantity of heat energy gained by the cooler object, provided that heat energy does not escape to the surroundings. The transfer of energy will continue in this way until both substances reach the same temperature.
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“Hot” Vocabulary
absolute zero - the lowest temperature possible, 0 Kelvin or -273°C. Absolute zero is the temperature where all molecular movement would stop and zero energy would be present. Absolute zero can never be reached.
calorimeter - special containers used to measure the exchange of heat when substances are mixed.
conduction - the transfer of energy (usually in solids) as particles collide with each other.
convection - the transfer of energy (in liquids and gases) by currents due to a difference in densities of substances at different temperatures.
heat - the transfer of thermal energy from one substance to another due to a difference in temperature.
heat engine - a device that turns heat energy into mechanical work.
heat pump - pumps heat from one location to another. A heat pump can remove heat from the inside of a building and pump it outside (similar to an air conditioner), or it can take heat from outside and pump it indoors.
kinetic energy - energy in motion. Kinetic energy is the greatest in gases and least in solids.
latent heat of fusion - the quantity of heat energy released when 1 kg of a substance changes from solid to liquid without changing temperature.
latent heat of vaporization - the quantity of heat energy released when 1 kg of a substance changes from liquid to vapor without changing temperature.
linear expansion - the expansion of solids due to a temperature change. This expansion depends on its initial length, temperature change, and the type of substance it is made from.
potential energy - stored energy. Potential energy is the greatest in solids and least in gases.
radiation - the transfer of energy through space by electromagnetic waves.
specific heat capacity - the quantity of heat (energy) needed to raise the temperature of unit of mass of a substance by a unit of temperature change.
temperature - the average of potential and kinetic energies in a substance.
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thermal energy - the total or sum of the potential and kinetic energies in a substance.
thermal expansion - the expanding of a substance due to an increase in temperature and the contracting of a substance due to a decrease in temperature.
thermal resistance - the ability of a given thickness of a substance to prevent heat transfer.
thermodynamics - the branch of physics that deals with the relationship between heat and other forms of energy.
