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31. An ideal gas is initially in state A, as shown in the PV diagram (above). The gas undergoes a transition from state A by the three different processes shown, where process III is isothermal. In which process is energy added to the gas?
(A) I only (B) III only (C) I and II only (D) II and III only
32. A sample of an ideal gas can be taken from state A to state B
through one of two processes, as shown in the graph of pressure P versus volume V (right). Which of the following will be the same for both processes?
(A) The average kinetic energy of the gas (B) The temperature of the gas at the end of the process (C) The thermal energy transferred to the gas by heating (D) The work done on the gas
33. Identical samples of gas initially have pressure 3P and volume 2V. The final temperature is equal to the initial temperature for which of the processes? (select 2 answers)
(A) A (B) B (C) C (D) D
34. Referring to the P-V diagram (right), how much work is done by the gas as it cycles once along
41. A container is filled with Helium gas to a pressure P at a temperature T. Oxygen, which has
atoms that are 4 times more massive than those of helium, is then added to the container until
the new pressure in the container is 2P at the same temperature T. The ratio of the average
speed of the helium atoms to the average speed of the Oxygen atoms is
(A) 4 to 1
(B) 2 to 1
(C) √2 to 1
(D) 1 to 1
42. A container is filled with Helium gas to a pressure P at a temperature T. Oxygen, which has atoms that are 4 times more massive than those of helium, is then added to the container until the new pressure in the container is 2P at the same temperature T. The ratio of the number of helium atoms to oxygen atoms in the container is
(A) 5 to 1 (B) 6 to 1 (C) 16 to 1 (D) 1 to 1
43. A sealed container of air is kept at a constant temperature. What will happen to the
speed/average kinetic energy of the molecules of air in the container as time passes?
(A) The molecules will obey the second law of thermodynamics. Eventually, there will be no
deviations in the speed of kinetic energy of the air molecules whatsoever.
(B) Some molecules will speed up and others will slow down, but the average speed and
kinetic energy will be constant.
(C) The molecules will slow down, decreasing their average kinetic energy.
(D) There will be no change
44. Two boxes of equal volume each contain the same quantity of an ideal gas. The first box is
much warmer than the second box. Which of the following statements MUST be true? (select 2
answers)
(A) The pressure in the first box is greater than the pressure in the second box
(B) There are more molecules in the first box than in the second box
(C) The boxes contain different types of gasses
(D) The molecules in the first box have a higher average kinetic energy than those in the
second box
45. During a thermodynamic process, 2,000 J of heat are removed from a gas while 600 J of work is
done by the gas. What is the change in internal energy of the gas?
46. The internal energy of a sample of confined helium gas is increased by 300 J. If the net amount
of work done on the sample by its surroundings was 240 J, how much heat was transferred
between the gas and its environment?
(A) 60 J absorbed
(B) 540 J absorbed
(C) 60 J dissipated
(D) 540 J dissipated
47. Ice is placed in an empty container in a room where the air temperature is 20°C and allow to melt. While the ice is melting the temperature of the water is…
(A) less than 0°C (B) 0°C (C) room temperature (D) greater than 0°C but less than room temperature
48. A gas undergoes an expansion in which 300 J of energy is added to the gas by heating. The internal energy of the gas changes from 600 J to 700 J. The work done by the gas is:
(A) 1,300 J (B) 900 J (C) 200 J (D) 100 J
49. Convection can occur in which of the following substances? (Select two answers)
(A) Solids
(B) Liquids
(C) Bose-Einstein Condensate
(D) Gasses
50. If the absolute temperature of a radiating object is doubled, by what factor does the rate of
energy emission change?
(A) 2
(B) 4
(C) 16
(D) 32
51. The product of pressure and volume is expressed most commonly in which of the following
52. A gas trapped in a container with a movable piston undergoes an adiabatic process. During this
process, the gas does about 1025 joules of work. Which of the following statements are true?
(select 2 answers)
(A) The internal energy of the system increases by 1025 J
(B) The temperature of the gas increases
(C) The temperature of the gas decreases
(D) The heat transferred in or out of the system is zero
53. At higher altitudes, the air is colder. Why does this happen?
(A) There are fewer air molecules at higher altitudes, so are less collisions between
molecules and the air loses energy quickly.
(B) As a quantity of air moves to a higher altitude, it experiences a decrease in pressure.
This causes the air to expand. Since no heat is being added, the internal energy of the
air drops, and therefore its temperature drops.
(C) There are fewer people living in higher altitudes, at much of the warmth of our planet
comes from human emissions like body heat and greenhouse gasses that are heavily
concentrated in more populated areas.
(D) It is not colder in higher altitudes.
54. Which statement must be true regarding two systems of unequal temperature that come in
contact with one another?
(A) The final temperature will be the average of the two systems’ temperatures
(B) The final temperature will be greater than that of the warmer system
(C) There will be a decrease in total energy
(D) The total amount of thermal energy will be constant
55. An engine has an efficiency of 20% and produces 2000 J of mechanical work during one cycle. How much energy is transferred out of the engine by heating the environment during one cycle?
(A) 100 J
(B) 2000 J
(C) 8000 J
(D) 10000 J
Questions 56-58: A Carnot engine takes 2000 J of heat from a reservoir at 200∘𝐶, does some work, and
releases some heat into a second reservoir at 20°𝐶.