Deck 19: The Kinetic Theory of Gases

Question 1

A sample of an ideal gas is compressed by a piston from 10 m³ to 5 m³ and simultaneously cooled from 273 $\degree$ C to 0 $\degree$ C. 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

Answer 1

an increase in density

Question 2

An automobile tire is pumped up to a gauge pressure of 2.0 * 10⁵ Pa when the temperature is 27 $\degree$ C. What is its gauge pressure after the car has been running on a hot day so that the tire temperature is 77 $\degree$ C? Assume that the volume remains fixed and take atmospheric pressure to be 1.013 *10⁵ Pa.

A) 1.6 *10⁵ Pa
B) 2.6 *10⁵ Pa
C) 3.6 *10⁵ Pa
D) 5.9*10⁵ Pa
E) 7.9 * 10⁵ Pa

Answer 2

1.6 *10⁵ Pa

Question 3

Air enters a hot-air furnace at 7 $\degree$ C and leaves at 77 $\degree$ C. If the pressure does not change each entering cubic foot of air expands to:

A) 0.80 m³
B) 1.25 m³
C) 1.9 m³
D) 7.0 m³
E) 11 m³

Answer 3

1.25 m³

Question 4

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) isovolumic
D) isobaric
E) a closed cycle with point 1 coinciding with point 2

Question 5

A 2-m³ weather balloon is loosely filled with helium at 1 atm (76 cm Hg) and at 27 $\degree$ C. 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 -48 $\degree$ C, the gas volume (in m³) is:

A) 3
B) 4
C) 2
D) 2.5
E) 5.3

Question 6

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) 0.2 liters
B) 5.4 liters
C) 13.6 liters
D) 20.8 liters
E) none of these

Question 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

Question 8

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

Question 9

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

Question 10

273 cm³ of an ideal gas is at 0 $\degree$ C. It is heated at constant pressure to 10 $\degree$ C. It will now occupy:

A) 263 cm³
B) 273 cm³
C) 283 cm³
D) 278 cm³
E) 293 cm³

Question 11

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

Question 12

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 is what property of the gas?

A) Pressure
B) Density
C) Molecular kinetic energy
D) Internal energy
E) Temperature

Question 13

Oxygen (molar mass = 32 g) occupies a volume of 12 liters when its temperature is 20 $\degree$ C and its pressure is 1 atm. Using R = 0.082 liter . atm/mole. K, calculate the mass of the oxygen:

A) 6.4 g
B) 10.7 g
C) 16 g
D) 32 g
E) 64 g

Question 14

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) $\int$ p dV
E) V dp

Question 15

A quantity of an ideal gas is compressed to half its initial volume. The process may be adiabatic, isothermal or isobaric. Rank those three processes in order of the work required of an external agent, least to greatest.

A) adiabatic, isothermal, isobaric
B) adiabatic, isobaric, isothermal
C) isothermal, adiabatic, isobaric
D) isobaric, adiabatic, isothermal
E) isobaric, isothermal, adiabatic

Question 16

Use R = 8.2 *10^-5 m³ . atm/mol . K and N_A = 6.02 * 10²³ mol^-1. The approximate number of air molecules in a 1 m³ volume at room temperature (300 K) and atomospheric pressure is:

A) 41
B) 450
C) 2.5 * 10²⁵
D) 2.7 *10²⁶
E) 5.4 *10²⁶

Question 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 theperatures?

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

Question 18

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

Question 19

It is known that 28 grams of a certain ideal gas occupy 22.4 liters at standard conditions (0 $\degree$ C, 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

Question 20

In order that a single process be both isothermal and isobaric:

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

Question 21

In a certain gas the molecules are 5.0 *10^-9m apart on average, have a mean free path of 5.0 * 10^-6m, and have an average speed of 500m/s. The rate at which a molecule has collision with other molecules is about:

A) 10^-11 s^-1
B) 10^-8 s^-1
C) 1 s^-1
D) 10⁸ s^-1
E) 10¹¹ s^-1

Question 22

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

Question 23

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)
C)
D) increases by a factor of 2
E) decreases by a factor of 1/2

Question 24

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

Question 25

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

Question 26

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

Question 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

Question 28

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 *10^-7m. If the temperature is raised to 350 K and the pressure is reduced to 1.0 * 10⁴ Pa the mean free path is them:

A) 6.9 * 10^-8m
B) 9.3 *10 ^{- 8}m
C) 3.3 * 10 ^-7m
D) 1.7 *10^-6m
E) 2.3 *10^-6m

Question 29

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

Question 30

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

Question 31

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

Question 32

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

Question 33

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

Question 34

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

Question 35

A system consists of N gas molecules, each with mass m. Their rms speed is v_rms. Their total translational kinetic energy is:

A) (1/2)m(Nv_rms)²
B) (1/2)N(mv_rms)²
C) (1/2)mv²_rms
D) (1/2)Nmv²_rms
E) N[(1/2)mv_rms]²

Question 36

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

Question 37

The diagram shows three isotherms for an ideal gas, with T₃-T₂ the same as T₂-T₁. It also shows five thermodynamic processes caried out on the gas. Rank the processes in order 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 I, III, and IV tied, then II
D) IV, V, III, I, II
E) II, I, then III, IV, and V tied

Question 38

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

Question 39

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

Question 40

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

Question 41

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 v_A/v_B is:

A) 1/4
B) 1/2
C) 1
D) 2
E) 4

Question 42

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

Question 43

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

Question 44

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

Question 45

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

Question 46

The root-mean-square sped of molecules in a gas is:

A) the most probable speed
B) that speed such that half the molecules are moving faster than v_rms 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

Question 47

The temperature of low pressure hydrogen is reduced from 100 $\degree$ C to 20 $\degree$ C. The rms speed of its molecules decreases by approximately:

A) 80%
B) 89%
C) 46%
D) 21%
E) 11%

Question 48

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

Question 49

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

Question 50

The Maxwellian speed distribution provides a direct explanation of:

A) thermal expansion
B) the ideal gas law
C) heat
D) evaporation
E) boiling

Question 51

For a gas at thermal equilibrium the average speed v, the most probable speed v_p, and the root-mean-square speed v_rms are in the order:

A) v_p < v_rms < v
B) v_rms < v_p < v
C) v < v_rms < v_p
D) v_p < v < v_rms
E) v < v_p < v_rms

Question 52

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)

Question 53

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

Question 54

The average speed of air molecules at room temperature is about:

A) zero
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)

Question 55

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) 5.3 m/s
B) 5.7 m/s
C) 7.3 m/s
D) 28 m/s
E) 32 m/s

Question 56

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

Question 57

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 T_A/T_B is:

A) 1/4
B) 1/2
C) 1
D) 2
E) 4

Question 58

In a system of N gas molecules, the individual speeds are v₁, v₂, ..., v_N. The rms speed of these molecules is:

A)
B)
C)
D)
E)

Question 59

The rms speed of an oxygen molecule at 0 $\degree$ C 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 0 $\degree$ C is:

A) 230 m/s
B) 326 m/s
C) 650 m/s
D) 920 m/s
E) 1300 m/s

Question 60

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

Question 61

An ideal monatomic gas has a molar specific heat C_v at constant volume of:

A) R
B) 3R/2
C) 5R/2
D) 7R/2
E) 9R/2

Question 62

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 ΔE_{dia /} E_mon is:

A) 1/2
B) 3/5
C) 1
D) 5/3
E) 2

Question 63

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 remains 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) monatomic, diatomic

Question 64

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

Question 65

An ideal diatomic gas has a molar specific heat at constant pressure, C_p, of:

A) R
B) 3R/2
C) 5R/2
D) 7R/2
E) 9R/2

Question 66

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

Question 67

The number of degrees of freedom of a triatomic molecule is:

A) 1
B) 3
C) 6
D) 8
E) 9

Question 68

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 E_4m/E_m is:

A) 1/4
B) 1/2
C) 1
D) 2
E) 4

Question 69

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

Question 70

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

Question 71

The specific heat C_v 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
D) 1/2
E) 2

Question 72

An ideal gas has molar specific heat C_p at constant pressure. When the temperature of n moles is increased by $\Delta$ T the increase in the internal energy is:

A) nC_p $\Delta$ T
B) n(C_p + R) $\Delta$ T
C) n(C_p - R) $\Delta$ T
D) n(2C_p + R) $\Delta$ T
E) n(2C_p - R) $\Delta$ T

Question 73

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

Question 74

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 N_A
D) kT
E) RT

Question 75

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

Question 76

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 K_A/K_B is:

A) 1/4
B) 1/2
C) 1
D) 2
E) 4

Question 77

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) 1/2NkT
C) 3/2NkT
D) 5/2NkT
E) 3NkT

Question 78

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 T_A/T_B is:

A) 1/4
B) 1/2
C) 1
D) 2
E) 4

Question 79

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

Question 80

The number of degrees of freedom of a rigid diatomic molecule is:

A) 2
B) 3
C) 4
D) 5
E) 6