Thermal Physics
IB 12
Internal Energy: total potential energy and random kinetic energy of the molecules of a substance
Symbol:
Units:
Internal Kinetic Energy: arises from random translational, vibrational, and rotational motion
Internal Potential Energy: arises from forces between the molecules
Temperature (Definition #1): a measure of the average random kinetic energy of all the particles of a system
Symbol:
Units:
Conversion:
Thermal Energy (Heat): the transfer of energy between two substances by
non-mechanical means – conduction, convection and radiation
Symbol:
Units:
Before
After
Temperature (Definition #2): a property that determines the direction of thermal energy transfer between
two objects
Thermal Equilibrium:
Thermal Capacity:
Formula:
Symbol:
Units:
Symbol:
Units:
Specific Heat Capacity:
Formula:
Relationship:
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1. Compare the thermal capacities and specific heat capacities of these samples.
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Why do different amounts of the same substances have different
thermal capacities?
A
B
Why do the same amounts of different substances have different
specific heat capacities?
2. The thermal capacity of a sample of lead is 3.2 x 103 J K-1.
a) How much thermal energy will be released
if it cools from 610 C to 250 C?
b) What is the mass of the sample?
3. How much thermal energy is needed to raise the
temperature of 2.50 g of water from its freezing
point to its boiling point?
Slope
Compare your answer to the amount of thermal energy needed to
raise the temperature of liquid mercury the same amount.
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4. An active solar heater is used to heat 50 kg of water initially at 120 C. If the average rate that the thermal energy is absorbed in
a one hour period is 2.1 x 104 J min-1, determine the final temperature after one hour.
Why will the final temperature probably be less than what you calculated above?
5. A hole is drilled in an 800g iron block and an electric heater is placed inside. The heater provides thermal energy at a constant
rate of 600 W.
a) Assuming no thermal energy is lost to the surrounding environment, calculate how long it will take the iron block to
increase its temperature by 150 C.
b) The temperature of the iron block is recorded as it varies with time and is
shown at right. Comment on reasons for the shape of the graph.
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Calorimetry
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Conservation of Energy
Assumption:
1. A 0.10 kg sample of an unknown metal is heated to 1000 C by placing it in boiling water for a few
minutes. Then it is quickly transferred to a calorimeter containing 0.40 kg of water at 100 C.
After thermal equilibrium is reached, the temperature of the water is 150 C.
a) What is the specific heat capacity of the metal sample?
Method of Mixtures
b) What is the thermal capacity of the metal sample?
2. A 3.0 kg block of copper at 900 C is transferred to a calorimeter containing 2.00 kg of water at 200 C. The mass of the calorimeter
cup, also made of copper, is 0.210 kg. Determine the final temperature of the water.
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Phases of Matter
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Kinetic theory says that:
1. All matter is made up of atoms, and
2. the atoms are in continuous random motion at a variety of speeds.
3. Whether a substance is a solid, liquid, or gas basically depends on how close together its molecules are and how strong the
bonds are that hold them together.
Solid
Liquid
Macroscopic
description
Definite volume
Definite shape
Microscopic
description
Molecules are held in fixed
positions relative to each
other by strong bonds and
vibrate about a fixed point in
the lattice
Comparative
density
High
Kinetic energy
Vibrational
Potential energy
Average molecular
separation
Gas
Definite volume
Variable shape
Molecules are closely
packed with strong bonds
but are not held as rigidly in
place and can move relative
to each other as bonds break
and reform
Variable volume
Variable shape
Molecules are widely spaced
apart without bonds, moving
in random motion, and
intermolecular forces are
negligible except during
collisions
High
Low
High
Vibrational
Rotational
Some translational
Higher
Mostly translational
Higher rotational
Higher vibrational
Highest
Atomic radius
Atomic radius
10 x atomic radius
Molecules per m3
1028
1028
1025
Volume of
molecules/volume
of substance
1
1
10-3
Phase Changes
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IB 12
1. Describe and explain the process of phase changes in terms of molecular behavior.
When thermal energy is added to a solid, the molecules gain kinetic energy as they vibrate at an increased rate. This is seen
macroscopically as an increase in temperature. At the melting point, a temperature is reached at which the kinetic energy of
the molecules is so great that they begin to break the permanent bonds that hold them fixed in place and begin to move
about relative to each other. As the solid continues to melt, more and more molecules gain sufficient energy to overcome
the intermolecular forces and move about so that in time the entire solid becomes a liquid. As heating continues, the
temperature of the liquid increases due to an increase in the vibrational, translational and rotational kinetic energy of the
molecules. At the boiling point, a temperature is reached at which the molecules gain sufficient energy to overcome the
intermolecular forces that hold them together and escape from the liquid as a gas. Continued heating provides enough
energy for all the molecules to break their bonds and the liquid turns entirely into a gas. Further heating increases the
translational kinetic energy of the gas and thus its temperature increases.
2. Explain in terms of molecular behavior why temperature does not change during a phase change.
The making or breaking of intermolecular bonds involves energy. When bonds are broken (melting and vaporizing), the
potential energy of the molecules is increased and this requires input energy. When bonds are formed (freezing and
condensing), the potential energy of the molecules is decreased as energy is released. The forming or breaking of bonds
happens independently of the kinetic energy of the molecules. During a phase change, all energy added or removed from
the substance is used to make or break bonds rather than used to increase or decrease the kinetic energy of the molecules.
Thus, the temperature of the substance remains constant during a phase change.
3. Explain in terms of molecular behavior the process of evaporation.
Evaporation is a process by which molecules leave the surface of a liquid, resulting in the cooling of the
liquid. Molecules with high enough kinetic energy break the intermolecular bonds that hold them in the
liquid and leave the surface of the substance. The molecules that are left behind thus have a lower
average kinetic energy and the substance therefore has a lower temperature.
Factors affecting the rate of evaporation:
a) surface area
b) drafts
c) temperature
d) pressure
e) latent heat of vaporization
4. Distinguish between evaporation and boiling.
Evaporation – process whereby liquid turns to gas, as explained above
- occurs at any temperature below the boiling temperature
- occurs only at surface of liquid as molecules escape
- causes cooling of liquid
Boiling –
process whereby liquid turns to gas when the vapor pressure of the liquid equals the atmospheric
pressure of its surroundings
-
occurs at one fixed temperature, dependent on substance and pressure
-
occurs throughout liquid as bubbles form, rise to surface and are released
-
temperature of substance remains constant throughout process
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Specific Latent Heat
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Specific Latent Heat:
Symbol:
Units:
Formula:
Specific latent heat of fusion:
Specific latent heat of vaporization:
1. How much energy is needed to change 500 grams of ice into water?
a) Assume the ice is already at its melting point.
b) Assume the ice is at -150 C.
2. Thermal energy is supplied to a pan containing 0.30 kg of water at 200 C at a rate of 400 W for 10 minutes. Estimate the mass of
water turned into steam as a result of this heating process.
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3. The latent heat of vaporization of water is 2300 kJ/kg. How long would it take a 2 kW electric kettle containing
800g of boiling water to boil off all the water?
4. In order to maintain a constant body temperature, a sunbather need to lose about 320 J of thermal energy to the
environment every second through sweating. Estimate the amount of sweat evaporated from the skin of the
sunbather every second.
5. The cost of electricity is $0.15 per kWhr. How much does it cost to heat 1.0 m3 from 20o C to 25oC?
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The Kinetic Model of an Ideal Gas
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Kinetic theory views all matter as consisting of individual particles in continuous motion in an attempt to
relate the macroscopic behaviors of the substance to the behavior of its microscopic particles.
Certain microscopic assumptions need to be made in order to deduce the behavior of an ideal gas, that is, to
build the Kinetic Model of an Ideal Gas.
Assumptions:
1. A gas consists of an extremely large number of very tiny particles (atoms or molecules) that are in continuous random
motion with a variety of speeds.
2. The volume of the particles is negligible compared to the volume occupied by the entire gas.
3. The size of the particles is negligible compared to the distance between them.
4. Collisions between particles and collisions between particles and the walls of the container are assumed to be perfectly
elastic and take a negligible amount of time.
5. No forces act between the particles except when they collide (no intermolecular forces). As a consequence, the internal
energy of an ideal gas consists solely of random kinetic energy – no potential energy.
6. In between collisions, the particles obey Newton’s laws of motion and travel in straight lines at a constant speed.
Pressure
Macroscopic definition:
Formula:
Atmospheric Pressure
Units:
1. A cylinder with diameter 3.00 cm is open to the air.
What is the pressure on the gas in this open cylinder?
2. What is the pressure on the gas after a 500. gram
piston and a 5.00 kg block are placed on top?
Atmospheric pressure at sea level
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Explaining Macroscopic Behavior in terms of the Kinetic Model
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Pressure
Microscopic definition:
Explanation:
1) A particle collides with the wall of container and changes momentum. By Newton’s second law, a
change in momentum means there must have been a force by the wall on the particle.
2) By Newton’s third law, there must have been an equal and opposite force by the particle on the wall.
3) In a short interval of time, there will be a certain number of collisions so the average result of all these
collisions is a constant force on the container wall.
4) The value of this constant force per unit area is the pressure that the gas exerts on the container walls.
1. Macroscopic behavior: Ideal gases increase in temperature when their volume is decreased.
Microscopic explanation: As the volume is reduced, the walls of
the container move inward. Since the particles are now colliding
with a moving wall, the wall transfers momentum (and kinetic
energy) to the particles, making them rebound faster from the
moving wall. Thus the kinetic energy of the particles increases and
this means an increase in the temperature of the gas.
2. Macroscopic behavior: Ideal gases increase in pressure when more gas is added to the container.
Microscopic explanation: More gas means more gas particles in the container so there will be an increase in the number of
collisions with the walls in a given interval of time. The force from each particle remains the same but an increased number
of collisions in a given time means the pressure increases.
Microscopic explanation: The increased temperature means
the particles have, on average, more kinetic energy and are thus
moving faster. This means that the particles hit the walls more
often and, when they do, they exert a greater force on the walls
during the collision. For both these reasons, the total force on
the wall in a given time increases which means that the
pressure increases.
pressure
3. Macroscopic behavior: At a constant volume, ideal gases increase in pressure when their temperature increases.
temperature
Relationship:
Control =
10
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4. Macroscopic behavior: At a constant pressure, ideal gases increase in volume when their temperature increases.
volume
Microscopic explanation: A higher temperature means faster
moving particles that collide with the walls more often and with
greater force. However, if the volume of the gas is allowed to
increase, the rate at which these particles hit the walls will
decrease and thus the average force exerted on the walls by the
particles, that is, the pressure can remain the same.
Relationship:
temperature
Control =
pressure
temperature (0 C)
pressure
temperature (K)
Absolute Zero:
Kelvin scale of Temperature: an absolute scale of temperature in which 0 K is the absolute zero of temperature
Microscopic explanation: The decrease in volume
means the particles hit a given area of the wall more
often. The force from each particle remains the same
but an increased number of collisions in a given time
means the pressure increases.
pressure
5. Macroscopic behavior: At a constant temperature, ideal gases increase in pressure when their volume decreases.
Relationship:
volume
Control =
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Ideal Gas Equation of State
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Derivation:
Equation of State:
The “state” of a fixed amount of a gas is described by the values of its pressure, volume, and temperature.
Gas constant:
Ideal Gas:
Compare real gases to an ideal gas:
a)
b)
Combined Gas Law derivation:
Mole: an amount of a substance that contains as many particles as there are atoms in 12 grams of carbon-12.
Avogadro’s constant: the number of atoms in 12 g of carbon 12.
NA =
Molar mass:
As a general rule, the molar mass in grams of a substance is numerically equal to its mass number.
a) 1 mole of
7
3
Li
b) 2 moles of 27
13
Al
has a mass of
has a mass of
c) How atoms are in 8 grams of helium (mass number = 4)?
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IB 12
1. What is the volume occupied by 16 g of
oxygen (mass number = 8) at room
temperature and atmospheric pressure?
2. A weather balloon with a volume of 1.0 m3
contains helium (mass number = 4) at
atmospheric pressure and a temperature of
350 C. What is the mass of the helium in the
balloon?
3. A gas in a closed container is under a pressure
of 1 atm and a temperature of -173 oC. The gas
is then heated to 27 o C. What is the new
pressure of the gas?
4. Compare the thermal capacities of two ideal gases – one heated at constant volume and one heated at constant pressure.
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Thermodynamics
IB 12
Thermodynamics is the branch of physics that deals with the way in which a system interacts with its surroundings.
Thermodynamic System
Surroundings
State of the system
Internal energy: total potential energy and random kinetic energy of the molecules of a substance
Symbol:
Units:
Work: product of force and displacement in the direction of the force
Symbol:
Units:
Thermal Energy (Heat): the transfer of energy between two substances by non-mechanical means – conduction,
convection and radiation
Symbol:
Units:
The internal energy of a system can change by . . .
Definitions:
Q=
W=
ΔU =
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1. A sample of gas is heated with a Bunsen burner
and allowed to expand. If 400 J of thermal energy
are transferred to the gas during heating and the gas
does 100 J of work by expanding, what is the
resulting change in the internal energy of the gas?
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2. A sample of gas is warmed by placing it in a bath
of hot water, adding 400 J of thermal energy. At the
same time, 100 J of work is done compressing the
gas manually. What is the resulting change in the
internal energy of the gas?
Formula:
First Law of Thermodynamics:
NOTE: The First Law is a statement of . .
1. In each case, determine the change in the internal energy of the gas.
a) A gas gains 1500 J of heat from its surroundings, and
expands, doing 2200 J of work on the surroundings.
b) A gas gains 1500 J of heat at the same time as an external
force compresses it, doing 2200 J of work on it.
Internal energy of many substances depends on . . .
Internal energy of an ideal gas depends on . . .
a.
b.
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Four Common Thermal Processes
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1. An isobaric process is one that occurs
2. An isochoric (isovolumetric) process is one that occurs
3. An isothermal process is one that occurs
4. An adiabatic process is one that occurs
Isobaric Process
The gas in the cylinder is expanding
isobarically because the pressure is
held constant by the external
atmosphere and the weight of the
piston and the block. Heat can enter
or leave through the non-insulating
walls.
Isochoric
(Isovolumetric)
Process
The gas in the cylinder is being
heated isochorically since the
volume of the cylinder is held
fixed by the rigid walls.
Heat can enter or leave through
the non-insulating walls.
Isothermal Process
The gas in the cylinder is being
allowed to expand isothermally
since it is in contact with a
water bath (heat reservoir) that
keeps the temperature constant.
Heat can enter or leave through
the non-insulating walls.
Adiabatic
Process
The gas in the cylinder is
being compressed
adiabatically since the
cylinder is surrounded by an
insulating material.
Isobaric Process
Work Involved in a Volume Change at Constant Pressure
How is pressure held constant?
How is work done by the gas?
How much work is done by the gas if it expands at constant pressure?
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What does an isobaric process look like on a diagram of pressure vs. volume (P-V diagram)?
Expansion of gas
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Compression of gas
How can the amount of work done by a gas during a process be determined from a P-V diagram?
Isobaric Processes and the First Law of Thermodynamics
Expansion at
constant pressure
Gas laws:
1st law:
Example: A gas is allowed to expand
isobarically by adding 1000 J of thermal
energy, causing the gas to increase its internal
energy by 200 J. How much work is done by
the gas in expanding?
Compression at
constant pressure
Gas laws:
1st law:
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Isochoric (Isovolumetric) Process
Work:
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Gas law:
1st law:
1. One mole of an ideal gas is heated at a constant volume of 2.0 x 10-3 m3 from an initial pressure of 1.0 x 105 Pa to a final
pressure of 5.0 x 105 Pa.
a) Determine the initial and final temperatures of the gas.
b) Does the internal energy of the gas increase or decrease? Justify your answer.
c) Determine the work done by the gas during this process.
c) If the change in internal energy of the gas is 1200J, determine the amount of thermal energy added to the gas.
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2. In each case shown below, an ideal gas at 5.0 x 105 Pa and 1.0 x 10-3 m3 expands to 4.0 x 10-3 m3 at a
pressure of 1.0 x 105 Pa by a different process or series of processes.
I.
II.
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III.
a) Compare the change in internal energy of the gas as a result of each process. Justify your answer.
b) Compare the work done by (or on) the gas during each process. Justify your answer.
c) Compare the thermal energy added to or removed from the gas during each process. Justify your answer.
d) If the internal energy decreases in each case is 500 J, calculate the work done and thermal energy exchanged in each case.
Conclusions:
1)
2)
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Isothermal Process
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Heat reservoir:
1st Law:
Gas Law:
Expansion:
Compression:
Ideal Gas Equation of State
Isotherm:
Conclusions:
1)
2)
3)
Expansion
Compression
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Adiabatic Process
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Adiabatic walls:
NOTE:
1st Law:
Expansion:
Compression:
1. If 410 J of heat energy are added to an ideal gas
causing it expand at constant temperature,
2. If an ideal gas is allowed to expand adiabatically, the internal energy
of the gas changes by2500 J.
a) what is the change in internal energy of the gas?
a) Does the internal energy of the gas increase or decrease? Justify your
answer.
b) how much work is done by the gas?
Determine:
b) the thermal energy added or removed from the gas.
c) how much work is done on the gas?
c) the work done by the gas.
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IB 12
Cycles
Cycle:
The cycle shown below represents processes performed on an ideal gas initially at P0 = 1.0 x 105 Pa and V0 = 2.0 x 10-3 m3.
Q
ΔU
W
A→B
B→C
C→D
D→A
Cycle
1. Compare the temperatures at each state A, B, C, and D.
2. During process A→B, 600 J of thermal energy were added to the gas. Complete the chart.
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IB 12
Properties of the individual thermal processes
A→B
B→C
C→D
D→A
Net Work for a Cycle
Properties of the entire cycle
1)
2)
3)
4)
5)
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IB 12
An ideal gas is confined in a cylinder with a movable piston. The gas starts at
300 K in state A and proceeds through the cycle shown in the diagram.
a) Find the temperatures at B and at C.
b) State whether ΔU, W and Q are +, - , or 0 for each of the three processes and for the entire cycle.
Q
ΔU
W
A→B
B→C
C→A
Cycle
c) The internal energy of the gas changes by 1520 J during process A to B. 1700 J of heat are added to the gas
during process B to C. Find ΔU, W, and Q for each process and for the entire cycle.
Q
ΔU
W
A→B
B→C
C→A
Cycle
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The Second Law of Thermodynamics and Entropy
IB 12
The Second Law of Thermodynamics implies that . . .
Entropy:
Second Law of Thermodynamics:
1)
2)
Although local entropy can decrease, any process will increase the total entropy of a system and its surroundings (the universe).
1. Discuss this statement for the case of a puddle of water freezing into a block of ice.
2. A block of ice is placed in a thermally insulated room
initially at room temperature. Discuss any changes in the
total energy, total entropy, and temperature of the room.
3. An operating refrigerator with its door open is placed in a
thermally insulated room. The refrigerator operates for a long
period of time. Discuss any changes in the total energy, total
entropy, and temperature of the room.
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