1. Molar mass
You have a 1 g sample of hydrogen gas and helium gas.
Approximately how many moles and how many molecules do you have of each sample?

2. Atomic/molecular collisions and pressure
The kinetic-molecular theory relates pressure to elastic collisions between individual particles and the walls of the container.
Even though atoms/molecules are light, they move at hundreds or even thousands of m/s, and each contributes significant kinetic energy.

3. Q18.3
Consider two specimens of ideal gas at the same temperature. The molecules in specimen #1 have greater molar mass than the molecules in specimen #2. How do the rms speed of molecules (vrms) and the average translational kinetic energy per molecule (KE) compare in the two specimens?
A. vrms and KE are both greater in specimen #2.
B. vrms is greater in specimen #2; KE is the same in both specimens.
C. vrms is greater in specimen #2; KE is greater in specimen #1.
D. Both vrms and KE are the same in both specimens.
E. None of the above is correct.

4. A18.3
Consider two specimens of ideal gas at the same temperature. The molecules in specimen #1 have greater molar mass than the molecules in specimen #2. How do the rms speed of molecules (vrms) and the average translational kinetic energy per molecule (KE) compare in the two specimens?
A. vrms and KE are both greater in specimen #2.
B. vrms is greater in specimen #2; KE is the same in both specimens.
C. vrms is greater in specimen #2; KE is greater in specimen #1.
D. Both vrms and KE are the same in both specimens.
E. None of the above is correct.

5. Speed of air molecules
What is the average kinetic energy of one molecule of an ideal gas of oxygen (molar mass M = 32 g/mol) at 27°C? What about nitrogen (molar mass M = 28 g/mol)?
What is the rms speed of nitrogen and oxygen?

6. Measuring atomic/molecular speeds
Beams of molecules are created in a vacuum chamber where the pressure is low enough to have a mean free path at least 10 × farther than the sample path. (A typical apparatus would require 10−6 torr to obtain mean free path ~10–100 m and accommodate a 1 m experimental setup.)

7. Molecules form distributions of velocities
A temperature-dependent distribution forms around the most likely velocity for a given sample.

8. Ideal gas – Hydrogen
200 mg of hydrogen gas is in a 1 L container at twice atmospheric pressure. What is the temperature of the gas in degrees C?
If you double the temperature of the hydrogen gas, what is the new pressure?
Using the atomic model of gases, explain qualitatively why the pressure changes the way it does.

9. Car engine
In automobile engine, a mixture of air and gasoline is compressed in the cylinders before being ignited. A typical engine has a compression ratio of 9.00:1. The initial pressure is 1.00 atm and the initial temperature is 27°C. If pressure after compression is 21.7 atm, find the temperature of the compressed gas.

10. Q18.1
A quantity of an ideal gas is contained in a balloon. Initially the gas temperature is 27°C.
You double the pressure on the balloon and change the temperature so that the balloon shrinks to one-quarter of its original volume. What is the new temperature of the gas?
A. 54°C
B. 27°C
C. 13.5°C
D. –123°C
E. –198°C

11. A18.1
A quantity of an ideal gas is contained in a balloon. Initially the gas temperature is 27°C.
You double the pressure on the balloon and change the temperature so that the balloon shrinks to one-quarter of its original volume. What is the new temperature of the gas?
A. 54°C
B. 27°C
C. 13.5°C
D. –123°C
E. –198°C

12. Thermal processes
You have two identical samples of gas held at P1, V1. One sample undergoes an isothermal process that halves its volume, the other undergoes an isobaric process that halves its volume.
Draw the processes on a PV diagram and find final pressure and volume Pf and Vf for the two gas samples in terms of P1, V1. Which gas is at a higher temperature and by what factor?

13. Q18.2 p
This pV–diagram shows three possible states of a certain amount of an ideal gas.
Which state is at the highest temperature? 3 2 1
A. state #1
B. state #2
C. state #3
D. Two of these are tied for highest temperature.
E. All three of these are at the same temperature. V O

14. A18.2 p
This pV–diagram shows three possible states of a certain amount of an ideal gas.
Which state is at the highest temperature? 3 2 1
A. state #1
B. state #2
C. state #3
D. Two of these are tied for highest temperature.
E. All three of these are at the same temperature. V O

15. PV curves at constant temperature—isotherms
A single experiment can measure how pressure changes as volume changes. This is an isothermal curve.
Many isothermal curves together make a three-dimensional phase surface.
How do you predict from these graphs what happens to material in a sealed, rigid container if temperature is increased?

16. Does the path of the PV change matter?
The start, the finish, and the shape of the curve are all significant.

17. Compressed air
A compressed air cartridge at a starting pressure of p1 = 50 atm and starting volume V1 = 5 cm3 is put into an empty, sealed balloon. It pops and causes the balloon to expand to 10 times the volume of the cartridge, V2.
Assuming the air undergoes an isothermal expansion and behaves like an ideal gas, draw the pV diagram of this process.
What is the final pressure of the balloon p2?
Two other ways different than the first method 1) of inflating the balloon to the same final volume are 2) a constant pressure p1 = 50 atm inflates the balloon from V1 to V2 or 3) a constant pressure p2 (calculated above) inflates the balloon from V1 to V2. Draw pV diagrams and rank the work done on the expanding air for the three cases of expansion. E.g. W1>W2>W3

18. Study of thermodynamic processes
The cyclic process shown proceeds counterclockwise from a in the pV diagram to b and back and the total work is W = 500J.
Why is the work positive?
Find the change in thermal energy and the heat added during this process

19. Expanding Helium
Helium gas starts at a volume Vi = 1L = 0.001m3 and Pi = 1 atm. It expands linearly (on pV diagram) to Vf = 3L = 0.003m3 and Pf = 3 atm.
Draw the pV diagram for this process
What is the work done by the gas when it expands?
What is its increase in thermal energy?
How much heat is gained or lost by the gas?

20. Thermodynamic process definitions
Adiabatic
Isochoric
Isobaric
Isothermal

21. The processes on a PV diagram

22. Adiabatic changes
In an adiabatic process, no heat is transferred from system and surroundings.
Adiabatic process a – b:
Q = 0, DEth = W

23. Cyclic process
A cyclic thermodynamic process occurs as shown, where path c-b is isothermal. Draw isotherms to determine temperatures of states a, b, c. Predict the Q, W and DEth for each process: What changes if c-b is adiabatic? Q W
DEth
a-c
c-b
b-a
Whole cycle

24. Specific heat values

25. Q17.3.5
You put 1 kg of the following materials on a bunsen burner. Which one’s temperature rises the least?
A. Aluminum, c = 910 J/kg K
B. Berillium, c = 1970 J/kg K
C. Copper, c = 390 J/kg K
D. Water, c = 4190 J/kg K

26. A17.3.5
You put 1 kg of the following materials on a bunsen burner. Which one’s temperature rises the least?
A. Aluminum, c = 910 J/kg K
B. Berillium, c = 1970 J/kg K
C. Copper, c = 390 J/kg K
D. Water, c = 4190 J/kg K

27. Water in a teapot
A 500W heater dumps all its energy into heating 1kg of water in a teapot. How long does it take to heat the water to boiling if the water started out at room temperature?
How many moles of water is this?
cwater = 4190 J/kg K
Mwater = kg/mol

28. Phase changes and temperature behavior
A solid will absorb heat according to its heat capacity, becoming a hotter solid.
At the melting point, a solid will absorb its heat of fusion and become a liquid. An equilibrium mixture of a substance in both its liquid and solid phases will have a constant temperature.
A cold liquid will absorb heat according to its heat capacity to become a hotter liquid.
At the boiling point, a liquid will absorb its heat of vaporization and become a gas. An equilibrium mixture of liquid and gas will have a constant temperature.
A cold gas can absorb heat according to its heat capacity and become a hotter gas.

29. Q17.4
You wish to increase the temperature of a 1.00-kg block of a certain solid substance from 20°C to 25°C. (The block remains solid as its temperature increases.) To calculate the amount of heat required to do this, you need to know
A. the specific heat of the substance.
B. the molar heat capacity of the substance.
C. the heat of fusion of the substance.
D. the thermal conductivity of the substance.
E. more than one of the above

30. A17.4
You wish to increase the temperature of a 1.00-kg block of a certain solid substance from 20°C to 25°C. (The block remains solid as its temperature increases.) To calculate the amount of heat required to do this, you need to know
A. the specific heat of the substance.
B. the molar heat capacity of the substance.
C. the heat of fusion of the substance.
D. the thermal conductivity of the substance.
E. more than one of the above

31. Hot pot
A heavy copper pot of mass 2 kg is at temperature of 150C. You pour 0.1 kg of water at 25C into the pot then quickly close the lid so no steam can escape. Find the final temperature of the pot and its contents and determine the phase (liquid or gas) of the water. Assume no heat is lost to the surroundings.
cwater = 4190 J/kg K, ccopper = 390 J/kg K
Lwater = 2256 x 103 J/kg

32. Measuring heat capacities
Heat capacities may be measured at constant volume in a fairly complex process using a bomb calorimeter.
Heat capacities may be measured at constant pressure using equipment as simple as a coffee cup.

33. Illustration of heat absorption into degrees of freedom

34. How much heat energy can ensembles contain?
An atom can absorb energy as the kinetic energy of its motion.
A molecule can absorb energy in its translation, and also in its rotation and in the vibrations of one atom in its structure with respect to the others.
Atomic/molecular energy absorbed is termed its “heat capacity.”

35. Energy of monatomic and diatomic gases
How much heat is required to raise 4g of He gas from 300 K to 310 K at constant volume?
How about hydrogen gas H2?
What is the rms speed of He gas and H2 at 300K?

36. Relating heat capacities at constant volume and pressure
Q = DEth
Q = DEth - W

37. Heat capacities tabulated for selected gasses

38. Condensing steam
1671 cm3 of steam condenses to form 1 gram of water (1 cm3) when held at a constant pressure of 1 atm (1.013 x 105 Pa). The heat of vaporization at this pressure is Lv = x 106 J/kg.
Draw the pV diagram for this process
What is the work done by the water when it condenses?
What is its change in thermal energy?

39. Why, and how well, do materials transfer heat?
Conduction: heat transfer within a body or between two bodies in contact.
Convection: heat transfer through movement of mass from one place to another
Radiation: heat transfer by electromagnetic radiation

40. Convection of heat
Heating by moving large amounts of hot fluid, usually water or air.
Figure at right illustrates heat moving by convection.

41. Conduction of heat I
You bring a cooler to the beach to keep some tasty beverages cold. The cooler has a total wall area of 0.8 m2 and a wall thickness of 2.0 cm. It is filled with ice, water and your tasty beverage at 0C. What is the rate of heat flow into the cooler if the outside wall is at 30C?
How much ice melts in 8 hours? Assume the same rate of heat flow calculated above.