Deck 19: The Kinetic Theory of Gases

Question 1

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

Answer 1

the density of a gas becomes much greater when it is liquefied

Question 2

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

Answer 2

5.4 liters

Question 3

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

Answer 3

Density

Question 4

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 5

An automobile tire is pumped up to a gauge pressure of 2.0 * 10⁵ Pa when the temperature is 27°C.What is its gauge pressure after the car has been running on a hot day so that the tire temperature is 77°C? 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

Question 6

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

Question 7

A 2.0-m³ weather balloon is loosely filled with helium at 1 atm (76 cm Hg)and at 27°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°C, the gas volume is:

A)0.75 m³
B)1.3 m³
C)3.0 m³
D)4.0 m³
E)5.3 m³

Question 8

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

Question 9

It is known that 28 grams of a certain ideal gas occupy 22.4 liters at standard conditions (0°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 10

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 11

Oxygen (molar mass = 32 g)occupies a volume of 12 liters when its temperature is 20°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)11 g
C)16 g
D)32 g
E)64 g

Question 12

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 13

Air enters a hot-air furnace at 7°C and leaves at 77°C.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

Question 14

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

Question 15

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

Question 16

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 17

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

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

Question 18

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 atmospheric pressure is:

A)41
B)450
C)2.4 *10²⁵
D)2.7*10²⁶
E)5.4 * 10²⁶

Question 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

Question 20

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

Question 21

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 22

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 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

Question 24

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

Question 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)" V p dV"
E)"V dp"

Question 26

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

Question 27

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 28

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 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 29

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 30

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

Question 31

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 32

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

Question 33

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

Question 34

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

Question 35

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 36

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

Question 37

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

Question 38

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

Question 39

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

Question 40

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 41

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 42

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 43

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 44

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 45

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 46

The rms speed of an oxygen molecule at 0°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°C is:

A)160 m/s
B)330 m/s
C)650 m/s
D)1300 m/s
E)3700 m/s

Question 47

A certain ideal gas has a temperature 300 K and a pressure 5.0 *0 10⁴ Pa.The molecules have a mean free path of 4.0 *10 ^{- 7}m.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 *10 ^{- 8} m
B)9.3 *10 ^{- 8} m
C)3.4 *10 ^{- 7} m
D)1.7 *10 ^{- 6} m
E)2.3 *10 ^{- 6} m

Question 48

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

Question 49

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 50

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 51

The Maxwellian speed distribution provides a direct explanation of:

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

Question 52

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 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

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 55

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 56

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 57

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 58

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

Question 59

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

A)89%
B)79%
C)46%
D)21%
E)11%

Question 60

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 61

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 62

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 63

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 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

Question 65

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

Question 66

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 67

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 68

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)

Question 69

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 70

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)1/2
D)1
E)2

Question 71

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 72

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 73

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

Question 74

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 75

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 76

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 77

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 78

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 79

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 80

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