Chapter 19 Test Bank The Kinetic Theory of Gases - Fundamentals of Physics 11e Complete Test Bank by David Halliday. DOCX document preview.
Chapter: Chapter 19
Learning Objectives
LO 19.1.0 Solve problems related to Avogadro’s number.
LO 19.1.1 Identify Avogadro’s number NA.
LO 19.1.2 Apply the relationship between the number of moles n, the number of molecules N, and
Avogadro’s number NA.
LO 19.1.3 Apply the relationships between the mass m of a sample, the molar mass M of the molecules in the sample, the number of moles n in the sample, and Avogadro’s number NA.
LO 19.2.0 Solve problems related to ideal gases.
LO 19.2.1 Identify why an ideal gas is said to be ideal.
LO 19.2.2 Apply either of the two forms of the ideal gas law, written in terms of the number of moles n or the number of molecules N.
LO 19.2.3 Relate the ideal gas constant R and the Boltzmann constant k.
LO 19.2.4 Identify that the temperature in the ideal gas law must be in kelvins.
LO 19.2.5 Sketch p-V diagrams for a constant-temperature expansion of a gas and a constant-temperature contraction.
LO 19.2.6 Identify the term isotherm.
LO 19.2.7 Calculate the work done by a gas, including the algebraic sign, for an expansion and a contraction along an isotherm.
LO 19.2.8 For an isothermal process, identify that the change in internal energy ΔE is zero and that the energy Q transferred as heat is equal to the work W done.
LO 19.2.9 On a p-V diagram, sketch a constant-volume process and identify the amount of work done in terms of area on the diagram.
LO 19.2.10 On a p-V diagram, sketch a constant-pressure process and determine the work done in terms of area on the diagram.
LO 19.3.0 Solve problems related to pressure, temperature, and RMS speed.
LO 19.3.1 Identify that the pressure on the interior walls of a gas container is due to the molecular collisions with the walls.
LO 19.3.2 Relate the pressure on a container wall to the momentum of the gas molecules and the time intervals between their collisions with the wall.
LO 19.3.3 For the molecules of an ideal gas, relate the root-mean-square speed vrms and the average speed vavg.
LO 19.3.4 Relate the pressure of an ideal gas to the rms speed vrms of the molecules.
LO 19.3.5 For an ideal gas, apply the relationship between the gas temperature T and the rms speed vrms and molar mass M of the molecules.
LO 19.4.0 Solve problems related to translational kinetic energy.
LO 19.4.1 For an ideal gas, relate the average kinetic energy of the molecules to their rms speed.
LO 19.4.2 Apply the relationship between the average kinetic energy and the temperature of the gas.
LO 19.4.3 Identify that a measurement of a gas temperature is effectively a measurement of the average kinetic energy of the gas molecules.
LO 19.5.0 Solve problems related to mean free path.
LO 19.5.1 Identify what is meant by mean free path.
LO 19.5.2 Apply the relationship between the mean free path, the diameter of the molecules, and the number of molecules per unit volume.
LO 19.6.0 Solve problems related to the distribution of molecular speeds.
LO 19.6.1 Explain how Maxwell’s speed distribution law is used to find the fraction of molecules with speeds in a certain speed range.
LO 19.6.2 Sketch a graph of Maxwell’s speed distribution, showing the probability distribution versus speed and indicating the relative positions of the average speed vavg, the most probable speed vP, and the rms speed vrms.
LO 19.6.3 Explain how Maxwell’s speed distribution is used to find the average speed, the rms speed, and the most probable speed.
LO 19.6.4 For a given temperature T and molar mass M, calculate the average speed vavg, the most probable speed vP, and the rms speed vrms.
LO 19.7.0 Solve problems related to the molar specific heats of an ideal gas.
LO 19.7.1 Identify that the internal energy of an ideal monatomic gas is the sum of the translational kinetic energies of its atoms.
LO 19.7.2 Apply the relationship between the internal energy Eint of a monatomic ideal gas, the number of moles n, and the gas temperature T.
LO 19.7.3 Distinguish between monatomic, diatomic, and polyatomic ideal gases.
LO 19.7.4 For monatomic, diatomic, and polyatomic ideal gases, evaluate the molar specific heats for a constant-volume process and a constant-pressure process.
LO 19.7.5 Calculate a molar specific heat at constant pressure Cp by adding R to the molar specific heat at constant volume CV, and explain why (physically) Cp is greater.
LO 19.7.6 Identify that the energy transferred to an ideal gas as heat in a constant-volume process goes entirely into the internal energy (the random translational motion) but that in a constant-pressure process energy also goes into the work done to expand the gas.
LO 19.7.7 Identify that for a given change in temperature, the change in the internal energy of an ideal gas is the same for any process and is most easily calculated by assuming a constant-volume process.
LO 19.7.8 For an ideal gas, apply the relationship between heat Q, number of moles n, and temperature change ΔT, using the appropriate molar specific heat.
LO 19.7.9 Between two isotherms on a p-V diagram, sketch a constant-volume process and a constant-pressure process, and for each identify the work done in terms of area on the graph.
LO 19.7.10 Calculate the work done by an ideal gas for a constant-pressure process.
LO 19.7.11 Identify that the work done by a gas is zero for a constant-volume process.
LO 19.8.0 Solve problems related to degrees of freedom and molar specific heats.
LO 19.8.1 Identify that a degree of freedom is associated with each way a gas can store energy (translation, rotation, and oscillation).
LO 19.8.2 Identify that an energy of 1/2kT per molecule is associated with each degree of freedom.
LO 19.8.3 Identify that a monatomic gas can have an internal energy consisting of only translational motion.
LO 19.8.4 Identify that at low temperatures a diatomic gas has energy in only translational motion, at higher temperatures it also energy in molecular rotation, and at even higher temperatures it can also have energy in molecular oscillations.
LO 19.8.5 Calculate the molar specific heat for monatomic and diatomic ideal gases in a constant-volume process and a constant-pressure process.
LO 19.9.0 Solve problems related to the adiabatic expansion of an ideal gas.
LO 19.9.1 On a p-V diagram, sketch an adiabatic expansion (or contraction) and identify that there is no heat exchange Q with the environment.
LO 19.9.2 Identify that in an adiabatic expansion, the gas does work on the environment, decreasing the gas’s internal energy, and that in an adiabatic contraction, work is done on the gas, increasing the internal energy.
LO 19.9.3 In an adiabatic expansion or contraction, relate the initial pressure and volume to the final pressure and volume.
LO 19.9.4 In an adiabatic expansion or contraction, relate the initial temperature and volume to the final temperature and volume.
LO 19.9.5 Calculate the work done in an adiabatic process by integrating the pressure with respect to volume.
LO 19.9.6 Identify that a free expansion of a gas into a vacuum is adiabatic but no work is done and thus, by the first law of thermodynamics, the internal energy and temperature of the gas do not change.
Multiple Choice
1. Avogadro’s number is:
A) 6.02 x 1018 mol-1
B) 6.02 x 1020 mol-1
C) 6.02 x 1022 mol-1
D) 6.02 x 1023 mol-1
E) 6.02 x 1024 mol-1
Difficulty: E
Section: 19-1
Learning Objective 19.1.1
2. How many molecules are in a sample of 10-3 mol?
A) 6.02 x 1018
B) 6.02 x 1020
C) 6.02 x 1022
D) 6.02 x 1023
E) cannot tell without knowing the molecular mass
Difficulty: E
Section: 19-1
Learning Objective 19.1.2
3. Platinum has a molar mass of 195 g/mol. If you have a ring that contains 2.3 g of platinum, how many moles does it contain?
A) 0.012 mol
B) 85 mol
C) 450 mol
D) 7.2 x 1021 mol
E) 1.4 x 1024 mol
Difficulty: E
Section: 19.1
Learning Objective 19.1.3
4. Evidence that a gas consists mostly of empty space is the fact that:
A) the density of a gas becomes much greater when it is liquefied
B) gases exert pressure on the walls of their containers
C) gases are transparent
D) heating a gas increases the molecular motion
E) nature abhors a vacuum
Difficulty: E
Section: 19-2
Learning Objective 19.2.0
5. Air enters a hot-air furnace at 7C and leaves at 77C. If the pressure does not change each entering cubic meter of air expands to:
A) 0.80 m3
B) 1.25 m3
C) 1.9 m3
D) 7.0 m3
E) 11 m3
Difficulty: E
Section: 19-2
Learning Objective 19.2.2
6. 273 cm3 of an ideal gas is at 0C. It is heated at constant pressure to 10C. It will now occupy:
A) 263 cm3
B) 273 cm3
C) 278 cm3
D) 283 cm3
E) 293 cm3
Difficulty: E
Section: 19-2
Learning Objective 19.2.2
7. Two identical rooms in a house are connected by an open doorway. The temperatures in the two rooms are maintained at different values. Which room contains more air?
A) the room with higher temperature
B) the room with lower temperature
C) the room with higher pressure
D) neither because both have the same pressure
E) neither because both have the same volume
Difficulty: E
Section: 19-2
Learning Objective 19.2.2
8. It is known that 28 grams of a certain ideal gas occupy 22.4 liters at standard conditions (0C, 1 atm). The volume occupied by 42 grams of this gas at standard conditions is:
A) 14.9 liters
B) 22.4 liters
C) 33.6 liters
D) 42 liters
E) more data are needed
Difficulty: E
Section: 19-2
Learning Objective 19.2.2
9. An automobile tire is pumped up to a gauge pressure of 2.0 105 Pa when the temperature is 27C. What is its gauge pressure after the car has been running on a hot day so that the tire temperature is 77C? Assume that the volume remains fixed and take atmospheric pressure to be 1.013 105 Pa.
A) 1.6 105 Pa
B) 2.3 105 Pa
C) 2.5 105 Pa
D) 3.6 105 Pa
E) 8.6 105 Pa
Difficulty: E
Section: 19-2
Learning Objective 19.2.2
10. A sample of an ideal gas is compressed by a piston from 10 m3 to 5 m3 and simultaneously cooled from 273C to 0C. As a result there is:
A) an increase in pressure
B) a decrease in pressure
C) a decrease in density
D) no change in volume
E) an increase in density
Difficulty: E
Section: 19-2
Learning Objective 19.2.2
11. A 2.0-m3 weather balloon is loosely filled with helium at 1 atm (76 cm Hg) and at 27C. At an elevation of 20,000 ft, the atmospheric pressure is down to 38 cm Hg and the helium has expanded, being under no constraint from the confining bag. If the temperature at this elevation is –48C, the gas volume is:
A) 0.75 m3
B) 1.3 m3
C) 3.0 m3
D) 4.0 m3
E) 5.3 m3
Difficulty: E
Section: 19-2
Learning Objective 19.2.2
12. Oxygen (molar mass = 32 g) occupies a volume of 12 liters when its temperature is 20C and its pressure is 1 atm. Using R = 0.082 literatm/moleK, calculate the mass of the oxygen:
A) 6.4 g
B) 11 g
C) 16 g
D) 32 g
E) 64 g
Difficulty: M
Section: 19-2
Learning Objective 19.2.2
13. An ideal gas occupies 12 liters at 293 K and 1 atm (76 cm Hg). Its temperature is now raised to 373 K and its pressure increased to 215 cm Hg. The new volume is:
A) 3.3 liters
B) 5.4 liters
C) 27 liters
D) 46 liters
E) none of these
Difficulty: E
Section: 19-2
Learning Objective 19.2.2
14. Use R = 8.2 10–5 m3 atm/mol K and NA = 6.02 1023 mol–1. The approximate number of air molecules in a 1 m3 volume at room temperature (300 K) and atmospheric pressure is:
A) 41
B) 450
C) 2.4 1025
D) 2.7 1026
E) 5.4 1026
Difficulty: M
Section: 19-2
Learning Objective 19.2.2
15. An air bubble doubles in volume as it rises from the bottom of a lake (1000 kg/m3). Ignoring any temperature changes, the depth of the lake is:
A) 21 m
B) 0.76 m
C) 4.9 m
D) 10 m
E) 0.99 m
Difficulty: E
Section: 19-2
Learning Objective 19.2.2
16. An ideal gas undergoes an isothermal process starting with a pressure of 2 105 Pa and a volume of 6 cm3. Which of the following might be the pressure and volume of the final state?
A) 1 105 Pa and 10cm3
B) 3 105 Pa and 6 cm3
C) 4 105 Pa and 4 cm3
D) 6 105 Pa and 2 cm3
E) 8 105 Pa and 2 cm3
Difficulty: E
Section: 19-2
Learning Objective 19.2.2
17. The pressures p and volumes V of the five ideal gases, with the same number of molecules, are given below. Which has the highest temperature?
A) p = 1 105 Pa and V = 10cm3
B) p = 3 105 Pa and V = 6 cm3
C) p = 4 105 Pa and V = 4 cm3
D) p = 6 105 Pa and V = 2 cm3
E) p = 8 105 Pa and V = 2 cm3
Difficulty: E
Section: 19-2
Learning Objective 19.2.2
18. A given mass of gas is enclosed in a suitable container so that it may be maintained at constant volume. Under these conditions, there can be no change in what property of the gas?
A) Pressure
B) Density
C) Molecular kinetic energy
D) Internal energy
E) Temperature
Difficulty: E
Section: 19-2
Learning Objective 19.2.2
19. In order that a single process be both isothermal and occur at constant pressure:
A) one must use an ideal gas
B) such a process is impossible
C) a change of phase is essential
D) one may use any real gas such as N2
E) one must use a solid
Difficulty: E
Section: 19-2
Learning Objective 19.2.2
20. Over 1 cycle of a cyclic process in which a system does net work on its environment:
A) the change in the pressure of the system cannot be zero
B) the change in the volume of the system cannot be zero
C) the change in the temperature of the system cannot be zero
D) the change in the internal energy of the system cannot be zero
E) none of the above
Difficulty: E
Section: 19-2
Learning Objective 19.2.2
21. What is the relationship between the ideal gas constant R and the Boltzmann constant k?
A) R = nk/N
B) R = Nk/n
C) R = n/Nk
D) R = N/nk
E) depends on the molar specific heat of the gas
Difficulty: E
Section: 19-2
Learning Objective 19.2.3
22. In using the ideal gas law, the temperature T must be measured in:
A) Celsius
B) Kelvin
C) Fahrenheit
D) either Celsius or Kelvin
E) any units as long as the correct values of k or R are used
Difficulty: E
Section: 19-2
Learning Objective 19.2.4
23. An isothermal process for an ideal gas is represented on a p-V diagram by:
A) a horizontal line
B) a vertical line
C) a portion of an ellipse
D) a portion of a parabola
E) a hyperbola
Difficulty: E
Section: 19-2
Learning Objective 19.2.5
24. A real gas undergoes a process which can be represented as a curve on a p-V diagram. This curve is an isotherm if:
A) the volume of the gas does not change
B) the temperature of the gas does not change
C) the pressure of the gas does not change
D) the gas does no work on its environment
E) the gas exchanges no heat with its environment
Difficulty: E
Section: 19-2
Learning Objective 19.2.6
25. A real gas undergoes a process which can be represented as a curve on a p-V diagram. The work done by the gas during this process is:
A) pV
B) p(V2 – V1)
C) (p2 – p1)V
D) p dV
E) V dp
Difficulty: E
Section: 19-2
Learning Objective 19.2.7
26. The energy absorbed as heat by an ideal gas for an isothermal process equals:
A) the work done by the gas
B) the work done on the gas
C) the change in the internal energy of the gas
D) the negative of the change in internal energy of the gas
E) zero since the process is isothermal
Difficulty: E
Section: 19-2
Learning Objective 19.2.7
27. When an ideal gas undergoes a slow isothermal expansion:
A) the work done by the gas is the same as the energy absorbed as heat
B) the work done by the environment is the same as the energy absorbed as heat
C) the increase in internal energy is the same as the heat absorbed
D) the increase in internal energy is the same as the work done by the gas
E) the increase in internal energy is the same as the work done by the environment
Difficulty: M
Section: 19-2
Learning Objective 19.2.8
28. The pressure of an ideal gas is doubled during a process in which the energy given up as heat by the gas equals the work done on the gas. As a result, the volume is:
A) doubled
B) halved
C) unchanged
D) need more information to answer
E) nonsense, the process is impossible
Difficulty: M
Section: 19-2
Learning Objective 19.2.8
29. A real gas is changed slowly from state 1 to state 2. During this process no work is done on or by the gas. This process must be:
A) isothermal
B) adiabatic
C) occurring at constant volume
D) occurring at constant pressure
E) a closed cycle with point 1 coinciding with point 2
Difficulty: E
Section: 19-2
Learning Objective 19.2.9
30. A quantity of an ideal gas is compressed to half its initial volume. The process may be adiabatic, isothermal or occurring at constant pressure. Rank those three processes in order of the work required of an external agent, least to greatest.
A) adiabatic, isothermal, constant pressure
B) adiabatic, constant pressure, isothermal
C) isothermal, adiabatic, constant pressure
D) constant pressure, adiabatic, isothermal
E) constant pressure, isothermal, adiabatic
Difficulty: M
Section: 19-2
Learning Objective 19.2.10
31. The speeds of 25 molecules are distributed as follows: 5 in the range from 2 to 3 m/s, 10 in the range from 3 to 4 m/s, 5 in the range from 4 to 5 m/s, 3 in the range from 5 to 6 m/s, 1 in the range from 6 to 7 m/s, and 1 in the range from 7 to 8 m/s. Their average speed is about:
A) 2 m/s
B) 3 m/s
C) 4 m/s
D) 5 m/s
E) 6 m/s
Difficulty: E
Section: 19-3
Learning Objective 19.3.0
32. According to the kinetic theory of gases, the pressure of a gas is due to:
A) change of kinetic energy of molecules as they strike the wall
B) change of momentum of molecules as they strike the wall
C) average kinetic energy of the molecules
D) force of repulsion between the molecules
E) rms speed of the molecules
Difficulty: E
Section: 19-3
Learning Objective 19.3.1
33. The force on the walls of a vessel of a contained gas is due to:
A) repulsive force between gas molecules
B) slight loss in average speed of a gas molecule after collision with wall
C) change in momentum of a gas molecule due to collision with wall
D) elastic collisions between gas molecules
E) inelastic collisions between gas molecules
Difficulty: E
Section: 19-3
Learning Objective 19.3.1
34. A gas is confined to a cylindrical container of radius 1 cm and length 1 m. The pressure exerted on an end face, compared with the pressure exerted on the long curved face, is:
A) smaller because its area is smaller
B) smaller because most molecules cannot traverse the length of the cylinder without undergoing collisions
C) larger because the face is flat
D) larger because the molecules have a greater distance in which to accelerate before they strike the face
E) none of these
Difficulty: E
Section: 19-3
Learning Objective 19.3.2
35. Air is pumped into a bicycle tire at constant temperature. The pressure increases because:
A) more molecules strike the tire wall per second
B) the molecules are larger
C) the molecules are farther apart
D) each molecule is moving faster
E) each molecule has more kinetic energy
Difficulty: E
Section: 19-3
Learning Objective 19.3.2
36. Five molecules have speeds of 2.8, 3.2, 5.8, 7.3, and 7.4 m/s. Their root-mean-square speed is closest to:
A) 2.5 m/s
B) 5.3 m/s
C) 5.7 m/s
D) 28 m/s
E) 32 m/s
Difficulty: M
Section: 19-3
Learning Objective 19.3.3
37. In a system of N gas molecules, the individual speeds are v1, v2, ..., vN. The rms speed of these molecules is:
A)
B)
C)
D)
E)
Difficulty: E
Section: 19-3
Learning Objective 19.3.3
38. The root-mean-square speed of molecules in a gas is:
A) the most probable speed
B) that speed such that half the molecules are moving faster than vrms and the other half are moving slower
C) the average speed of the molecules
D) the square root of the square of the average speed
E) none of the above
Difficulty: E
Section: 19-3
Learning Objective 19.3.3
39. Oxygen has a molar mass of 32 g/mol. If 12 moles of oxygen are in a 0.1-m3 container with an rms speed of 480 m/s, what is the pressure of the gas?
A) 2.9 x 105 Pa
B) 2.1 x 106 Pa
C) 3.4 x 107 Pa
D) 2.9 x 108 Pa
E) 2.1 x 109 Pa
Difficulty: M
Section: 19-3
Learning Objective 19.3.4
40. The pressure of an ideal gas is doubled in an isothermal process. The root-mean-square speed of the molecules:
A) does not change
B) increases by a factor of
C) decreases by a factor of
D) increases by a factor of 2
E) decreases by a factor of 1/2
Difficulty: M
Section: 19-3
Learning Objective 19.3.5
41. The temperature of low pressure hydrogen is reduced from 100C to 20C. The rms speed of its molecules decreases by approximately:
A) 89%
B) 79%
C) 46%
D) 21%
E) 11%
Difficulty: M
Section: 19-3
Learning Objective 19.3.5
42. The mass of an oxygen molecule is 16 times that of a hydrogen molecule. At room temperature, the ratio of the rms speed of an oxygen molecule to that of a hydrogen molecule is:
A) 16
B) 4
C) 1
D) 1/4
E) 1/16
Difficulty: E
Section: 19-3
Learning Objective 19.3.5
43. The rms speed of an oxygen molecule at 0C is 460 m/s. If the molar mass of oxygen is 32 g and of helium is 4 g, then the rms speed of a helium molecule at 0C is:
A) 160 m/s
B) 330 m/s
C) 650 m/s
D) 1300 m/s
E) 3700 m/s
Difficulty: M
Section: 19-3
Learning Objective 19.3.5
44. A sample of argon gas (molar mass 40 g) is at four times the absolute temperature of a sample of hydrogen gas (molar mass 2 g). The ratio of the rms speed of the argon molecules to that of the hydrogen is:
A) 1
B) 5
C) 1/5
D)
E)
Difficulty: M
Section: 19-3
Learning Objective 19.3.5
45. If the molecules in a tank of hydrogen have the same rms speed as the molecules in a tank of oxygen, we may be sure that:
A) the pressures are the same
B) the hydrogen is at the higher temperature
C) the hydrogen is at the greater pressure
D) the temperatures are the same
E) the oxygen is at the higher temperature
Difficulty: E
Section: 19-3
Learning Objective 19.3.5
46. A system consists of N gas molecules, each with mass m. Their rms speed is vrms. Their total translational kinetic energy is:
A) (1/2)m(Nvrms)2
B) (1/2)N(mvrms)2
C) (1/2)mv2rms
D) (1/2)Nmv2rms
E) N[(1/2)mvrms]2
Difficulty: E
Section: 19-4
Learning Objective 19.4.1
47. An ideal gas is at a temperature of 320 K. What is the average translational kinetic energy of one of its molecules?
A) 9.2 x 10-24 J
B) 1.4 x 10-23 J
C) 2.1 x 10-23 J
D) cannot tell without knowing the molar mass
E) cannot tell without knowing whether the gas is monatomic or diatomic
Difficulty: E
Section: 19-4
Learning Objective 19.4.2
48. The temperature of a gas is most closely related to:
A) the kinetic energy of translation of its molecules
B) its total molecular kinetic energy
C) the sizes of its molecules
D) the potential energy of its molecules
E) the total energy of its molecules
Difficulty: E
Section: 19-4
Learning Objective 19.4.3
49. In a certain gas the molecules are 5.0 10-9 m apart on average, have a mean free path of 5.0 10-6 m, and have an average speed of 500 m/s. The rate at which a molecule has collision with other molecules is about:
A) 1011 s1
B) 108 s1
C) 1 s1
D) 108 s1
E) 1011 s1
Difficulty: M
Section: 19-5
Learning Objective 19.5.0
50. Evidence that molecules of a gas are in constant motion is:
A) winds exert pressure
B) two gases interdiffuse quickly
C) warm air rises
D) energy as heat is needed to vaporize a liquid
E) gases are easily compressed
Difficulty: E
Section: 19-5
Learning Objective 19.5.0
51. The mean free path of a gas molecule is:
A) the shortest dimension of the containing vessel
B) the cube root of the volume of the containing vessel
C) approximately the diameter of a molecule
D) average distance between adjacent molecules
E) average distance a molecule travels between intermolecular collisions
Difficulty: E
Section: 19-5
Learning Objective 19.5.1
52. The mean free path of molecules in a gas is:
A) the average distance they travel before escaping
B) the average distance they travel between collisions
C) the greatest distance they travel between collisions
D) the shortest distance they travel between collisions
E) the average distance they travel before splitting apart
Difficulty: E
Section: 19-5
Learning Objective 19.5.1
53. The average speeds v and molecular diameters d of five ideal gases are given below. The number of molecules per unit volume is the same for all of them. For which is the collision rate the greatest?
A) v = v0 and d = d0
B) v = 2v0 and d = d0/2
C) v = 3v0 and d = d0
D) v = v0 and d = 2d0
E) v = 4v0 and d = d0/2
Difficulty: E
Section: 19-5
Learning Objective 19.5.2
54. The mean free path of air molecules at room temperature and atmospheric pressure is about:
A) 10–3 m
B) 10–5 m
C) 10–7 m
D) 10–9 m
E) 10–11 m
Difficulty: E
Section: 19-5
Learning Objective 19.5.2
55. The mean free path of molecules in a gas is proportional to:
A) the molecular cross-sectional area
B) the reciprocal of the molecular cross-sectional area
C) the root-mean-square molecular speed
D) the square of the average molecular speed
E) the molar mass
Difficulty: E
Section: 19-5
Learning Objective 19.5.2
56. The mean free path of molecules in a gas is proportional to:
A) the molecular diameter
B) the reciprocal of the molecular diameter
C) the molecular concentration
D) the reciprocal of the molecular concentration
E) the average molecular speed
Difficulty: E
Section: 19-5
Learning Objective 19.5.2
57. If the temperature T of an ideal gas is increased at constant pressure the mean free path:
A) decreases in proportion to 1/T
B) decreases in proportion to 1/T2
C) increases in proportion to T
D) decreases in proportion to T2
E) does not change
Difficulty: M
Section: 19-5
Learning Objective 19.5.2
58. A certain ideal gas has a temperature 300 K and a pressure 5.0 104 Pa. The molecules have a mean free path of 4.0 107m. If the temperature is raised to 350 K and the pressure is reduced to 1.0 104 Pa the mean free path is then:
A) 6.9 108 m
B) 9.3 108 m
C) 3.4 107 m
D) 1.7 106 m
E) 2.3 106 m
Difficulty: M
Section: 19-5
Learning Objective 19.5.2
59. Which of the following changes when the pressure of an ideal gas is changed isothermally?
A) Mean free path
B) Root-mean-square molecular speed
C) Internal energy
D) Most probable kinetic energy
E) Average speed
Difficulty: E
Section: 19-5
Learning Objective 19.5.2
60. The Maxwellian speed distribution provides a direct explanation of:
A) thermal expansion
B) the ideal gas law
C) heat
D) evaporation
E) boiling
Difficulty: E
Section: 19-6
Learning Objective 19.6.0
61. According to the Maxwellian speed distribution, as the temperature increases the number of molecules with speeds within a small interval near the most probable speed:
A) increases
B) decreases
C) increases at high temperatures and decreases at low
D) decreases at high temperatures and increases at low
E) stays the same
Difficulty: E
Section: 19-6
Learning Objective 19.6.0
62. For a gas at thermal equilibrium the average speed v, the most probable speed vp, and the root-mean-square speed vrms are in the order:
A) vp < vrms < v
B) vrms < vp < v
C) v < vrms < vp
D) vp < v < vrms
E) v < vp < vrms
Difficulty: E
Section: 19-6
Learning Objective 19.6.2
63. The average speed of air molecules at room temperature is about:
A) 0 m/s
B) 2 m/s (walking speed)
C) 30 m/s (fast car)
D) 500 m/s (supersonic airplane)
E) 3 108 m/s (speed of light)
Difficulty: E
Section: 19-6
Learning Objective 19.6.4
64. According to the Maxwellian speed distribution, as the temperature increases the most probable speed:
A) increases
B) decreases
C) increases at high temperatures and decreases at low
D) decreases at high temperatures and increases at low
E) stays the same
Difficulty: E
Section: 19-6
Learning Objective 19.6.4
65. According to the Maxwellian speed distribution, as the temperature increases the average speed:
A) increases
B) decreases
C) increases at high temperatures and decreases at low
D) decreases at high temperatures and increases at low
E) stays the same
Difficulty: E
Section: 19-6
Learning Objective 19.6.4
66. Two ideal monatomic gases are in thermal equilibrium with each other. Gas A is composed of molecules with mass m while gas B is composed of molecules with mass 4m. The ratio of the average molecular speeds vA/vB is:
A) 1/4
B) 1/2
C) 1
D) 2
E) 4
Difficulty: E
Section: 19-6
Learning Objective 19.6.4
67. Ideal monatomic gas A is composed of molecules with mass m while ideal monatomic gas B is composed of molecules with mass 4m. The average molecular speeds are the same if the ratio of the temperatures TA/TB is:
A) 1/4
B) 1/2
C) 1
D) 2
E) 4
Difficulty: E
Section: 19-6
Learning Objective 19.6.4
68. As the pressure in an ideal gas is increased isothermally the average molecular speed:
A) increases
B) decreases
C) increases at high temperature, decreases at low
D) decreases at high temperature, increases at low
E) stays the same
Difficulty: M
Section: 19-6
Learning Objective 19.6.4
69. As the volume of an ideal gas is increased at constant pressure the average molecular speed:
A) increases
B) decreases
C) increases at high temperature, decreases at low
D) decreases at high temperature, increases at low
E) stays the same
Difficulty: M
Section: 19-6
Learning Objective 19.6.4
70. The heat capacity at constant volume of an ideal gas depends on:
A) the temperature
B) the pressure
C) the volume
D) the number of molecules
E) none of the above
Difficulty: E
Section: 19-7
Learning Objective 19.7.0
71. The internal energy of an ideal gas depends on:
A) the temperature only
B) the pressure only
C) the volume only
D) the temperature and pressure only
E) temperature, pressure, and volume
Difficulty: E
Section: 19-7
Learning Objective 19.7.1
72. Two monatomic ideal gases are in thermal equilibrium with each other. Gas A is composed of molecules with mass m while gas B is composed of molecules with mass 4m. The ratio of the average molecular kinetic energy KA/KB is:
A) 1/4
B) 1/2
C) 1
D) 2
E) 4
Difficulty: M
Section: 19-7
Learning Objective 19.7.1
73. Ideal monatomic gas A is composed of molecules with mass m while ideal monatomic gas B is composed of molecules with mass 4m. The average molecular energies are the same if the ratio of the temperatures TA/TB is:
A) 1/4
B) 1/2
C) 1
D) 2
E) 4
Difficulty: M
Section: 19-7
Learning Objective 19.7.1
74. The diagram shows three isotherms for an ideal gas, with T3-T2 the same as T2-T1. It also shows five thermodynamic processes carried out on the gas. Rank the processes in order of the change in the internal energy of the gas, least to greatest.
A) I, II, III, IV, V
B) V; then I, III and IV tied; then II
C) V; I; then III, and IV tied; then II
D) II; then I, III and IV tied; then V
E) II; I; then III, IV, and V tied
Difficulty: E
Section: 19-7
Learning Objective 19.7.2
75. Two ideal gases, each consisting of N monatomic molecules, are in thermal equilibrium with each other and equilibrium is maintained as the temperature is increased. A molecule of the first gas has mass m and a molecule of the second has mass 4m. The ratio of the internal energies E4m/Em is:
A) 1/4
B) 1/2
C) 1
D) 2
E) 4
Difficulty: E
Section: 19-7
Learning Objective 19.7.2
76. Both the pressure and volume of an ideal gas of diatomic molecules are doubled. The ratio of the new internal energy to the old both measured relative to the internal energy at 0 K is:
A) 1/4
B) 1/2
C) 1
D) 2
E) 4
Difficulty: M
Section: 19-7
Learning Objective 19.7.2
77. The pressure of an ideal gas of diatomic molecules is doubled by halving the volume. The ratio of the new internal energy to the old, both measured relative to the internal energy at 0 K, is:
A) 1/4
B) 1/2
C) 1
D) 2
E) 4
Difficulty: M
Section: 19-7
Learning Objective 19.7.2
78. An ideal monatomic gas has a molar specific heat Cv at constant volume of:
A) R
B) 3R/2
C) 5R/2
D) 7R/2
E) 9R/2
Difficulty: E
Section: 19-7
Learning Objective 19.7.4
79. The specific heat Cv at constant volume of a monatomic gas at low pressure is proportional to Tn where the exponent n is:
A) –1
B) 0
C) 1/2
D) 1
E) 2
Difficulty: E
Section: 19-7
Learning Objective 19.7.4
80. The ratio of the specific heat of an ideal gas at constant volume to its specific heat at constant pressure is:
A) R
B) 1/R
C) dependent on the temperature
D) dependent on the pressure
E) different for monatomic, diatomic, and polyatomic gases
Difficulty: E
Section: 19-7
Learning Objective 19.7.4
81. The specific heat at constant volume of an ideal gas depends on:
A) the temperature
B) the pressure
C) the volume
D) the number of molecules
E) none of the above
Difficulty: E
Section: 19-7
Learning Objective 19.7.4
82. Consider the ratios of the heat capacities = Cp/Cv for the three types of ideal gases: monatomic, diatomic, and polyatomic.
A) is the greatest for monatomic gases
B) is the greatest for polyatomic gases
C) is the same only for diatomic and polyatomic gases
D) is the same only for monatomic and diatomic gases
E) is the same for all three
Difficulty: E
Section: 19-7
Learning Objective 19.7.4
83. An ideal gas has molar specific heat Cp at constant pressure. When the temperature of n moles is increased by T the increase in the internal energy is:
A) nCpT
B) n(Cp + R)T
C) n(Cp – R)T
D) n(2Cp + R)T
E) n(2Cp – R)T
Difficulty: E
Section: 19-7
Learning Objective 19.7.5
84. The heat capacity at constant volume and the heat capacity at constant pressure have different values because:
A) heat increases the internal energy at constant volume but not at constant pressure
B) heat increases the internal energy at constant pressure but not at constant volume
C) the system does work at constant volume but not at constant pressure
D) the system does work at constant pressure but not at constant volume
E) the system does more work at constant volume than at constant pressure
Difficulty: E
Section: 19-7
Learning Objective 19.7.5
85. The difference between the molar specific heat at constant pressure and the molar specific heat at constant volume for an ideal gas is:
A) the Boltzmann constant k
B) the universal gas constant R
C) the Avogadro number NA
D) kT
E) RT
Difficulty: E
Section: 19-7
Learning Objective 19.7.5
86. The ratio of the specific heat of a gas at constant volume to its specific heat at constant pressure is:
A) 1
B) less than 1
C) more than 1
D) has units of pressure/volume
E) has units of volume/pressure
Difficulty: E
Section: 19-7
Learning Objective 19.7.5
87. Energy transferred into an ideal gas as heat:
A) goes entirely into the internal energy of the gas
B) goes entirely into doing work to expand the gas
C) goes entirely into the internal energy of the gas only if the pressure is constant
D) goes entirely into the internal energy of the gas only if the temperature is constant
E) goes entirely into the internal energy of the gas only if the volume is constant
Difficulty: E
Section: 19-7
Learning Objective 19.7.6
88. For a given change in temperature, the change in the internal energy of an ideal gas:
A) also depends on the change in pressure
B) also depends on the change in volume
C) depends on whether the process is adiabatic or not
D) depends on whether the process occurs at constant pressure or not
E) can be calculated assuming the volume is constant
Difficulty: E
Section: 19-7
Learning Objective 19.7.7
89. Assume that helium behaves as an ideal monatomic gas. If 2 moles of helium undergo a temperature increase of 100 K at constant pressure, how much energy has been transferred to the helium as heat?
A) 1700 J
B) 2500 J
C) 4200 J
D) 5000 J
E) 6700 J
Difficulty: M
Section: 19-7
Learning Objective 19.7.8
90. Assume that helium behaves as an ideal monatomic gas. If 2 moles of helium undergo a temperature increase of 100 K at constant pressure, how much work is done by the gas?
A) 0 J
B) 1700 J
C) 2500 J
D) 4200 J
E) 5000 J
Difficulty: E
Section: 19-7
Learning Objective 19.7.10
91. Assume that helium behaves as an ideal monatomic gas. If 2 moles of helium undergo a temperature increase of 100 K at constant volume, how much work is done by the gas?
A) 0 J
B) 1700 J
C) 2500 J
D) 4200 J
E) 5000 J
Difficulty: E
Section: 19-7
Learning Objective 19.7.11
92. The number of degrees of freedom of a rigid diatomic molecule is:
A) 2
B) 3
C) 4
D) 5
E) 6
Difficulty: E
Section: 19-8
Learning Objective 19.8.0
93. The number of degrees of freedom of a triatomic molecule is:
A) 1
B) 3
C) 6
D) 8
E) 9
Difficulty: E
Section: 19-8
Learning Objective 19.8.0
94. The "Principle of equipartition of energy" states that the internal energy of a gas is shared equally:
A) among the molecules
B) between kinetic and potential energy
C) among the relevant degrees of freedom
D) between translational and vibrational kinetic energy
E) between temperature and pressure
Difficulty: E
Section: 19-8
Learning Objective 19.8.1
95. The specific heat of a polyatomic gas is greater than the specific heat of a monatomic gas because:
A) the polyatomic gas does more positive work when energy is absorbed as heat
B) the monatomic gas does more positive work when energy is absorbed as heat
C) the energy absorbed by the polyatomic gas is split among more degrees of freedom
D) the pressure is greater in the diatomic gas
E) a monatomic gas cannot hold as much heat
Difficulty: E
Section: 19-8
Learning Objective 19.8.1
96. An ideal gas of N diatomic molecules has temperature T. If the number of molecules is doubled without changing the temperature, the internal energy increases by:
A) 0
B) NkT
C) NkT
D) NkT
E) 3 NkT
Difficulty: E
Section: 19-8
Learning Objective 19.8.2
97. A monatomic gas can have internal energy consisting of:
A) translational motion only
B) rotational motion only
C) oscillatory motion only
D) both translational and rotational motion
E) translational, rotational, and oscillatory motion, depending on temperature
Difficulty: E
Section: 19-8
Learning Objective 19.8.3
98. A diatomic gas can have internal energy consisting of:
A) translational motion only
B) rotational motion only
C) oscillatory motion only
D) both translational and rotational motion
E) translational, rotational, and oscillatory motion, depending on temperature
Difficulty: E
Section: 19-8
Learning Objective 19.8.4
99. An ideal diatomic gas has a molar specific heat at constant pressure, Cp, of:
A) R
B) 3R/2
C) 5R/2
D) 7R/2
E) 9R/2
Difficulty: E
Section: 19-8
Learning Objective 19.8.5
100. An ideal gas of N monatomic molecules is in thermal equilibrium with an ideal gas of the same number of diatomic molecules and equilibrium is maintained as temperature is increased. The ratio of the changes in the internal energies ΔEdia / ΔEmon is:
A) 1/2
B) 3/5
C) 1
D) 5/3
E) 2
Difficulty: M
Section: 19-8
Learning Objective 19.8.5
101. Three gases, one consisting of monatomic molecules, the second consisting of diatomic molecules, and the third consisting of polyatomic molecules, are in thermal equilibrium with each other and remain in thermal equilibrium as the temperature is raised. All have the same number of molecules. The gases with the least and greatest internal energy are respectively:
A) polyatomic, monatomic
B) monatomic, polyatomic
C) diatomic, monatomic
D) polyatomic, diatomic
E) all have equal internal energy
Difficulty: E
Section: 19-8
Learning Objective 19.8.5
102. When work W is done on an ideal gas of N diatomic molecules in thermal isolation the temperature increases by:
A) W/2Nk
B) W/3Nk
C) 2W/3Nk
D) 2W/5Nk
E) W/Nk
Difficulty: M
Section: 19-8
Learning Objective 19.8.5
103. When work W is done on an ideal gas of diatomic molecules in thermal isolation the increase in the total rotational energy of the molecules is:
A) 0
B) W/3
C) 2W/3
D) 2W/5
E) W
Difficulty: M
Section: 19-8
Learning Objective 19.8.5
104. When work W is done on an ideal gas of diatomic molecules in thermal isolation the increase in the total translational kinetic energy of the molecules is:
A) 0
B) 2W/3
C) 2W/5
D) 3W/5
E) W
Difficulty: M
Section: 19-8
Learning Objective 19.8.5
105. The temperature of n moles of an ideal monatomic gas is increased by T at constant pressure. The energy Q absorbed as heat, change Eint in internal energy, and work W done by the environment are given by:
A) Q = (5/2)nRT, Eint = 0, W = –nRT
B) Q = (3/2)nRT, Eint = (5/2)nRT, W = –(3/2)nRT
C) Q = (5/2)nRT, Eint = (5/2)nRT, W = 0
D) Q = (3/2)nRT, Eint = 0, W = –nRT
E) Q = (5/2)nRT, Eint = (3/2)nRT, W = –nRT
Difficulty: M
Section: 19-8
Learning Objective 19.8.5
106. The temperature of n moles of an ideal monatomic gas is increased by T at constant volume. The energy Q absorbed as heat, change Eint in internal energy, and work W done by the environment are given by:
A) Q = (5/2)nRT, Eint = 0, W = 0
B) Q = (3/2)nRT, Eint = (3/2)nRT, W = 0
C) Q = (3/2)nRT, Eint = (1/2)nRT, W = –nRT
D) Q = (5/2)nRT, Eint = (3/2)nRT, W = –nRT
E) Q = (3/2)nRT, Eint = 0, W = –(3/2)nRT
Difficulty: M
Section: 19-8
Learning Objective 19.8.5
107. TV is constant for an ideal gas undergoing an adiabatic process, where is the ratio of heat capacities Cp/Cv. This is a direct consequence of:
A) the zeroth law of thermodynamics alone
B) the zeroth law and the ideal gas equation of state
C) the first law of thermodynamics alone
D) the ideal gas equation of state alone
E) the first law and the equation of state
Difficulty: E
Section: 19-9
Learning Objective 19.9.0
108. During a slow adiabatic expansion of a gas:
A) the pressure remains constant
B) energy is added as heat
C) work is done on the gas
D) no energy enters or leaves as heat
E) the temperature is constant
Difficulty: E
Section: 19-9
Learning Objective 19.9.1
109. An adiabatic process for an ideal gas is represented on a p-V diagram by:
A) a horizontal line
B) a vertical line
C) a hyperbola
D) a circle
E) none of these
Difficulty: E
Section: 19-9
Learning Objective 19.9.1
110. In an adiabatic expansion,
A) the temperature of the gas does not change.
B) the gas does work on the environment, and the internal energy of the gas decreases.
C) the environment does work on the gas, and the internal energy of the gas increases.
D) the volume of the gas does not change.
E) the pressure of the gas does not change.
Difficulty: E
Section: 19-9
Learning Objective 19.9.2
111. In an adiabatic contraction,
A) the temperature of the gas does not change.
B) the gas does work on the environment, and the internal energy of the gas decreases.
C) the environment does work on the gas, and the internal energy of the gas increases.
D) the volume of the gas does not change.
E) the pressure of the gas does not change.
Difficulty: E
Section: 19-9
Learning Objective 19.9.2
112. During a reversible adiabatic expansion of an ideal gas, which of the following is NOT true?
A) = constant
B) pV = nRT
C) = constant
D) W = – pdV
E) pV = constant
Difficulty: E
Section: 19-9
Learning Objective 19.9.3
113. Monatomic, diatomic, and polyatomic ideal gases each undergo slow adiabatic expansions from the same initial volume and the same initial pressure to the same final volume. The magnitude of the work done by the environment on the gas:
A) is greatest for the polyatomic gas
B) is greatest for the diatomic gas
C) is greatest for the monatomic gas
D) is the same only for the diatomic and polyatomic gases
E) is the same for all three gases
Difficulty: E
Section: 19-9
Learning Objective 19.9.5
114. If a gas expands freely into a vacuum,
A) the expansion is adiabatic, so the gas does work on its environment and its internal energy decreases.
B) the expansion is isothermal.
C) the expansion is occurs at constant pressure.
D) the expansion is adiabatic but no work is done, so the internal energy of the gas and its temperature both decrease.
E) the expansion is adiabatic but no work is done, so the internal energy of the gas and its temperature do not change.
Difficulty: E
Section: 19-9
Learning Objective 19.9.6