Deck 17: Temperature and the Kinetic Theory of Gases

Question 1

Calculate the point on the Fahrenheit scale when numerically it is 100 degrees larger than that of the Celsius scale for the same temperature.

A) 85
B) 265
C) 185
D) 165
E) no such point exists

Answer 1

185

Question 2

Normal human body temperature is 98.6ºF. What is the corresponding Celsius temperature?

A) 54.8ºC
B) 72.6ºC
C) 40.0ºC
D) 37.0ºC
E) 35.5ºC

Answer 2

37.0ºC

Question 3

An example of a thermometric property is

A) the volume of a gas.
B) the pressure of a confined gas.
C) the electrical resistance of an electrical conductor.
D) the length of a column of mercury.
E) All of these are correct.

Answer 3

All of these are correct.

Question 4

The temperature of the air on a hot day when the temperature is 108ºF is

A) 10ºC
B) 110ºC
C) 32 K
D) 315 K
E) 420 K

Question 5

If it is known that two bodies are in thermal equilibrium, one can conclude that

A) they must be in thermal equilibrium with a third body.
B) there must be a net heat flow between them.
C) the bodies must be at different temperatures.
D) some shared physical property must be changing.
E) they must be at the same temperature.

Question 6

An interval of 30 kelvins is equivalent to an interval of

A) 30 Fahrenheit degrees.
B) 76 Fahrenheit degrees.
C) 577 Fahrenheit degrees.
D) 303 Fahrenheit degrees.
E) None of these is correct.

Question 7

The temperature at which the Celsius and Fahrenheit scales read the same is

A) 40ºC
B) -40ºC
C) 20ºF
D) 68ºF
E) 100ºC

Question 8

A constant-volume gas thermometer reads 6.66 kPa at the triple point of water. What is the pressure reading at the normal boiling point of water?

A) 2.44 kPa
B) 18.2 kPa
C) 9.10 kPa
D) 11.8 kPa
E) 4.87 kPa

Question 9

The temperature in January in Winnipeg, Manitoba, has been known to go down to -40ºC. What is this temperature on the Fahrenheit scale?

A) -40ºF
B) -104ºF
C) +9.8ºF
D) -72ºF
E) -32ºF

Question 10

If it is known that two bodies are in thermal equilibrium, one can conclude that

A) they must be in thermal equilibrium with a third body.
B) there must be a net heat flow between them.
C) the bodies must be at different temperatures.
D) some shared physical property must be changing.
E) None of these is correct.

Question 11

The graph shows the natural logarithm of the temperature of various thermometers as a function of time. The thermometer that cools at the quickest rate is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 12

A thermometer is constructed by filling a small glass tube with a liquid that expands linearly with temperature. The thermometer is then calibrated at 0 ^$\circ$ C and 100 ^$\circ$ C, and the scale evenly divided between the two values. Unfortunately a manufacturing defect results in the middle one-third of the tube being narrower, otherwise the tube has uniform diameter. For what range of temperatures is the reading accurate?

A) 0 ^$\circ$ C to 33 ^$\circ$ C
B) 0 ^$\circ$ C and 67 ^$\circ$ C
C) 0 ^$\circ$ C to 33 ^$\circ$ C and 67 ^$\circ$ C to 100 ^$\circ$ C
D) 67 ^$\circ$ C to 100 ^$\circ$ C
E) At no point does this thermometer gives the right reading except at 0 ^$\circ$ C and 100 ^$\circ$ C.

Question 13

If you plot a graph with Fahrenheit temperatures along the horizontal axis and the corresponding Celsius temperatures along the vertical axis, the slope of the equal-temperature line will be

A) -40 Fº/Cº
B) 32 Fº/Cº
C) 1.8 Fº/Cº
D) 0.56 Fº/Cº
E) 0 Fº/Cº

Question 14

Which of the following statements about absolute zero temperature is true?

A) At absolute zero all translational motion of the particles ceases.
B) At absolute zero all rotational motion of the particles ceases.
C) Absolute zero is defined at - 273.15 ^$\circ$ C.
D) At absolute zero all the particles are at rest, except for the quantum motion.
E) All the above.

Question 15

Which curve correctly represents the relation of the temperature in degrees Fahrenheit to the temperature in degrees Celsius?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 16

A temperature difference of 5 Cº is the same as a difference of

A) 41 Fº
B) 14 Fº
C) 9 Fº
D) 5 Fº
E) -15 Fº

Question 17

A temperature of 14ºF is equivalent to

A) -10ºC
B) 7.77ºC
C) 25.5ºC
D) 26.7ºC
E) 47.7ºC

Question 18

The highest and lowest temperatures ever recorded in the United States are 134ºF (California, 1913) and -80ºF (Alaska, 1971). What are these temperatures in kelvins?

A) 407 K and 193 K
B) 330 K and 211 K
C) 347 K and 228 K
D) 340 K and 300 K
E) 365 K and 246 K

Question 19

A temperature difference of 9ºF is the same as a difference of

A) 5ºC
B) 9ºC
C) 20ºC
D) 68ºC
E) 100ºC

Question 20

Which of the following statements about thermal contact and thermal equilibrium is NOT true?

A) Two objects can be in thermal equilibrium even if they are not in thermal contact with each other.
B) Heat may be transferred between two objects when they are in thermal contact.
C) For energy to be transferred between two objects they have to be in thermal contact.
D) Thermal contact between two objects allows energy to be transferred without the use of macroscopic work.
E) Two objects, one that feels cold and the other does not feel as cold, does not imply that they are not in thermal equilibrium.

Question 21

The air in a balloon occupies a volume of 0.10 m³ when at a temperature of 27ºC and a pressure of 1.2 atm. What is the balloon's volume at 7ºC and 1.0 atm? (The amount of gas remains constant.)

A) 0.022 m³
B) 0.078 m³
C) 0.089 m³
D) 0.11 m³
E) 0.13 m³

Question 22

The temperature of the air on a cold day when the temperature is 23ºF is

A) 100 K
B) -5ºC
C) 273 K
D) 373 K
E) -15ºF

Question 23

If the pressure and volume of an ideal gas are both reduced to half their original value, the absolute temperature of the gas is

A) unchanged.
B) doubled.
C) halved.
D) increased by a factor of 4.
E) decreased by a factor of 4.

Question 24

If a mass of oxygen gas occupies a volume of 8 L at standard temperature and pressure, what is the change in the volume if the temperature is decreased to 136 K and the pressure remains constant?

A) It increases to 16 L.
B) It decreases to 12 L.
C) It increases to 24 L.
D) It decreases to 4 L.
E) It increases to 12 L.

Question 25

Assume that helium is a perfect gas and that the volume of a cylinder containing helium is independent of temperature. A cylinder of helium at +85ºC has a pressure of 208 atm. The pressure of the helium when it is cooled to -55ºC is

A) -132 atm
B) 127 atm
C) 335 atm
D) 132 atm
E) 204 atm

Question 26

A rigid container of air is at atmospheric pressure and 27ºC. To double the pressure in the container, heat it to

A) 54ºC
B) 300ºC
C) 327ºC
D) 600ºC
E) 327 K

Question 27

A gas has a density X at standard temperature and pressure. What is the new density when the absolute temperature is doubled and the pressure increased by a factor of 3?

A) (2/3)X
B) (4/3)X
C) (3/4)X
D) (6)X
E) (3/2)X

Question 28

A gas thermometer could measure temperature change by measuring the change in

A) density at constant volume.
B) specific heat at constant volume.
C) pressure at constant volume.
D) volume at constant temperature.
E) mass at constant volume.

Question 29

The relationship between the pressure and the volume of a gas expressed by Boyle's law holds true

A) for some gases under any conditions.
B) if the density is constant.
C) if the container of the gas can expand with increasing pressure.
D) if the temperature is constant.
E) for all gases under any conditions.

Question 30

The graph shows the natural logarithm of the temperature of various thermometers as a function of time. The thermometer that cools at the slowest rate is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 31

You can double both the pressure and the volume of an ideal gas if you change the temperature of the gas by

A) reducing it to one-quarter of its original value.
B) doubling it.
C) reducing it to one-half of its original value.
D) quadrupling it.
E) doing none of these

Question 32

A collection of oxygen molecules occupies a volume V at standard temperature and pressure. What is the new volume if the amount of oxygen is doubled and the pressure is tripled?

A) V
B) (2/3)V
C) (3/2)V
D) 6V
E) (5/9)V

Question 33

In a vacuum system, a container is pumped down to a pressure of 1.33 $\times$ 10^-6 Pa at 20ºC. How many molecules of gas are there in 1 cm³ of this container? (Boltzmann's constant k = 1.38 $\times$ 10^-23 J/K)

A) 3.3 $\times$ 10⁸
B) 4.8 $\times$ 10⁹
C) 3.3 $\times$ 10¹⁴
D) 7.9 $\times$ 10¹²
E) 4.8 $\times$ 10¹²

Question 34

If both the temperature and the volume of an ideal gas are doubled, the pressure is

A) increased by a factor of 4.
B) doubled also.
C) unchanged.
D) diminished by a factor of ¼.
E) None of these is correct.

Question 35

Inside a sphere of radius 12 cm are 8.0 $\times$ 10²³ gas molecules at a temperature of 50 ^$\circ$ C. What pressure do the gas molecules exert on the inside of the sphere?

A) 650 $\times$ 10³ Pa
B) 370 $\times$ 10³ Pa
C) 76.0 $\times$ 10³ Pa
D) 160 $\times$ 10³ Pa
E) 490 $\times$ 10³ Pa

Question 36

A large balloon is being filled with He from gas cylinders. The temperature is 25 ^$\circ$ C and the pressure is 1 atmosphere. The volume of the inflated balloon is 2500 m³. What was the volume of He in the cylinders if the gas was under a pressure of 110 atmospheres and at a temperature of 12 ^$\circ$ C when in the gas cylinders?

A) 11 m³
B) 22 m³
C) 24 m³
D) 15 m³
E) 23 m³

Question 37

If a mass of oxygen gas occupies a volume of 8 L at standard temperature and pressure, what is the change in the volume if the temperature is reduced by one half and the pressure is doubled?

A) It increases to 12 L.
B) It decreases to 6 L.
C) It increases to 24 L.
D) It decreases to 2 L.
E) It does not change.

Question 38

What mass of He gas occupies 8.5 liters at 0 ^$\circ$ C and 1 atmosphere? (The molar mass of He = 4.00 g/mol.)

A) 10.5 g
B) 0.66 g
C) 2.6 g
D) 0.38 g
E) 1.52 g

Question 39

Which of the following statements about the ideal gas law, PV = nRT, is NOT true?

A) When the temperature of two low density gases, which are initially at the same temperature, pressure and volume, is increased by the same amount, the volume increases by the same amount.
B) When the volume of two low density gases, which are initially at the same temperature, pressure and volume, is compressed by the same amount, the temperature increases by the same amount.
C) A P-T plot of any gas at low density intercept the T-axis at the same point.
D) The intercept at the ordinate for PV/nT vs P plot of any gas is the gas constant.
E) The ideal gas law is valid for high density of all gases.

Question 40

A mass of He gas occupies a volume V at standard temperature and pressure. What volume is occupied if the mass is halved, the absolute temperature doubled, and the pressure increased by a third?

A) (3/16)V
B) (4/3)V
C) (3/4)V
D) (3/8)V
E) (1/3)V

Question 41

At what common Celsius temperature is the rms velocity of oxygen molecules (molar mass = 32 g/mol) double that of hydrogen molecules (molar mass = 2.0 g/mol)?

A) -50
B) zero
C) no such temperature exists
D) 2.0
E) 16

Question 42

At what Kelvin temperature does the rms speed of the oxygen (O₂) molecules in the air near the surface of the earth become equal to the escape speed from the earth? (R = 8.31 J/mol · K; molar mass of O₂ gas is 32 g/mol; radius of the earth R_E = 6.37 $\times$ 10⁶ m; the escape speed from the earth is 11.2 km/s)

A) 4.8 $\times$ 10⁵ K
B) 8.0 $\times$ 10⁴ K
C) 1.6 $\times$ 10⁵ K
D) 1.1 $\times$ 10⁴ K
E) 3.6 $\times$ 10⁵ K

Question 43

A mass of air is at pressure P and volume V at 1ºC. When it is made to occupy half this volume at three times this pressure, its temperature becomes approximately

A) 411ºC
B) 0.67ºC
C) 1.5ºC
D) 6ºC
E) 411 K

Question 44

Boltzmann's constant, k, has a value of 1.381 $\times$ 10^-23 J/K. What is the significance of the constant?

A) It defines a characteristic energy at the microscopic level given the temperature in kelvins.
B) It allows the pressure of the gas to be calculated given the volume and temperature.
C) It measures the average kinetic energy of a molecule at a given temperature for each degree of freedom.
D) (A) and (B)
E) (A) and (C)

Question 45

If you carry a sealed cylinder of oxygen to the moon, you should expect no change in the oxygen's

A) mass.
B) weight.
C) temperature.
D) pressure.
E) rms molecular velocity.

Question 46

The air around us has 78% nitrogen and 21% oxygen. If the pressure is 1 atm, the pressure due to oxygen is

A) 0.21 atm
B) 0.78 atm
C) 1 atm
D) 0.5 atm
E) 0.67 atm

Question 47

An ideal gas whose original temperature and volume are 27ºC and 0.283 m³ undergoes an isobaric expansion. If the final temperature is 87ºC, then the final volume is approximately

A) 0.0340 m³
B) 0.0552 m³
C) 0.170 m³
D) 0.340 m³
E) 1.45 m³

Question 48

The oxygen (molar mass = 32 g/mol) and nitrogen (molar mass = 28 g/mol) molecules in this room have equal average

A) kinetic energies, but the oxygen molecules are faster.
B) kinetic energies, but the oxygen molecules are slower.
C) kinetic energies and speeds.
D) speeds, but the oxygen molecules have a higher average kinetic energy.
E) speeds, but the oxygen molecules have a lower average kinetic energy.

Question 49

A hailstorm causes an average pressure of 1.4 N/m² on the 200-m² flat roof of a house. The hailstones, each of mass 7.0 $\times$ 10^-3 kg, have an average velocity of 10 m/s perpendicular to the roof and rebound after hitting the roof with the same speed. How many hailstones hit the roof each second?

A) 4000
B) 2000
C) 1000
D) 10
E) 800

Question 50

At room temperature, which of the following diatomic molecules has the greater average kinetic energy: carbon monoxide (molar mass = 28 g/mol), nitrogen (molar mass = 28 g/mol), or oxygen (molar mass = 32 g/mol)?

A) carbon monoxide
B) nitrogen
C) oxygen
D) Both a and b are correct.
E) All three have the same average kinetic energy.

Question 51

If the absolute temperature of a gas is doubled, what is the change in the rms speed of its molecules?

A) no change
B) increases by a factor of 2
C) decreases by a factor of 2
D) increases by a factor of
E) decreases by a factor of

Question 52

A cylinder contains oxygen gas at a temperature of 7ºC and a pressure of 15 atm in a volume of 100 L. A fitted piston is lowered into the cylinder, decreasing the volume occupied by the gas to 80 L and raising the temperature to 40ºC. The gas pressure is now approximately

A) 3040 atm
B) 595 atm
C) 108 atm
D) 21 atm
E) 17 atm

Question 53

Two monoatomic gases, helium and neon, are mixed in the ratio of 2 to 1 and are in thermal equilibrium at temperature T (the molar mass of neon = 5 $\times$ the molar mass of helium). If the average kinetic energy of each helium atom is U, calculate the average energy of each neon atom.

A) U
B) 0.5U
C) 2U
D) 5U
E) U/5

Question 54

Ethyl chloride (C₂H₅Cl) is used as a refrigerant under certain circumstances. One mole of this substance contains Avogadro's number of

A) carbon atoms.
B) hydrogen atoms.
C) chlorine atoms.
D) All of these are correct.
E) None of these is correct.

Question 55

If the absolute temperature of a gas is doubled, what is the change in the average kinetic energy of its molecules?

A) no change
B) increases by a factor of 2
C) decreases by a factor of 2
D) increases by a factor of
E) decreases by a factor of

Question 56

A room measures 3 m $\times$ 4 m $\times$ 2 m and is at 15 ^$\circ$ C and 1 atm. When the temperature is increased to 25 ^$\circ$ C, the number of molecules that escaped from the room is, assuming that the pressure stays at 1 atm

A) 6.1 $\times$ 10²⁶
B) 2.1 $\times$ 10²⁵
C) 2.9 $\times$ 10²⁶
D) 1.2 $\times$ 10²⁸
E) 7.04 $\times$ 10²⁷

Question 57

Two monoatomic gases, helium and neon, are mixed in the ratio of 2 to 1 and are in thermal equilibrium at temperature T (the molar mass of helium = 4.0 g/mol and the molar mass of neon = 20.2 g/mol). If the average kinetic energy of each helium atom is 6.3 $\times$ 10^-21 J, calculate the temperature T.

A) 304 K
B) 456 K
C) 31 K
D) 31 ^$\circ$ C
E) 101 K

Question 58

Doubling the Kelvin temperature of a gas increases which of the following measures of its molecular velocity by a factor of 1.4?

A) the rms speed
B) the average speed
C) the most probable speed
D) All three of these speeds are correct.
E) None of these is correct.

Question 59

A cylinder of volume 50 L contains oxygen gas at a pressure of 2 atm. If nitrogen gas of volume 25 L and at pressure 1 atm is added to the oxygen cylinder, the new pressure is

A) 2 atm
B) 3 atm
C) 2.5 atm
D) 3.5 atm
E) 4 atm

Question 60

One mole of hydrogen gas (molar mass = 2.0 g/mol) has an rms velocity of 2.0 $\times$ 10³ m/s. To what temperature on the Celsius scale does this correspond?

A) 4.8 $\times$ 10⁴
B) 3.2 $\times$ 10²
C) 3.2 $\times$ 10⁵
D) 48
E) 69

Question 61

The rms speed of oxygen molecules is 460 m/s at 0ºC. The molecular weight of oxygen is 8 times the molecular weight of helium. The rms speed of helium at 40ºC is approximately

A) 3.68 km/s
B) 1.84 km/s
C) 1.40 km/s
D) 880 m/s
E) 440 m/s

Question 62

On the basis of the kinetic theory of gases, when the absolute temperature is doubled, the average kinetic energy of the gas molecules changes by a factor of

A) 16
B) 2
C)
D) 4
E) 0.5

Question 63

A 1 L container contains O₂ gas at STP. If the diameter of the O₂ molecule is 3.75 $\times$ 10 ^-10 m, the number of collisions per second is

A) 6.7 $\times$ 10⁹
B) 6.1 $\times$ 10⁹
C) 8.1 $\times$ 10⁹
D) 7.1 $\times$ 10⁹
E) 1.0 $\times$ 10¹⁰

Question 64

In a Maxwell-Boltzmann distribution function of molecular speeds, the rms speed is

A) always greater than the mean speed.
B) always less than the mean speed.
C) equal to the mean speed.
D) equal to the most probable speed.
E) independent of the temperature.

Question 65

Use the following to answer question:
The figure shows the distribution of the molecular speeds of a gas for two different temperatures.

A) The curve labeled T₁ represents the distribution for the higher temperature molecules.
B) The point labeled "1" corresponds to the rms speed of the molecules whose temperature is T₁.
C) The point labeled "2" corresponds to the maximum speed of the molecules whose temperature is T₁.
D) The point labeled "3" corresponds to the average speed of the molecules whose temperature is T₁.
E) None of these is correct.

Question 66

Which of the following is an assumption that is made in the kinetic theory of gases?

A) Molecules are not described by Newton's laws.
B) Molecules make up only a small fraction of the volume occupied by a gas.
C) Molecules collide inelastically.
D) The total number of molecules is actually very small.
E) There are forces acting on the molecules at all times.

Question 67

If the rms speed of oxygen molecules is 460 m/s at 0ºC, the rms speed of oxygen molecules at 273ºC is approximately

A) 230 m/s
B) 325 m/s
C) 650 m/s
D) 920 m/s
E) 1.84 km/s

Question 68

A volume of an ideal gas goes through a temperature change from 20ºC to 60ºC. The relation between the average molecular kinetic energy at 20ºC (K₁) and that at 60ºC (K₂) is

A) K₁ = K₂
B) K₁ = 0.33 K₂
C) K₁ = 3 K₂
D) K₁ = 0.88 K₂
E) K₁ = 1.14 K₂

Question 69

Which of the following is NOT an assumption made in the kinetic theory model of a gas?

A) A gas consists of particles called molecules.
B) The molecules are in random motion and their behavior is described by Newton's laws.
C) The range of molecular forces is much greater than the molecular size.
D) Between collisions, molecules travel with constant speed and in a straight line.
E) Collisions are perfectly elastic and are of negligible duration.

Question 70

A room measures 3 m $\times$ 4 m $\times$ 2 m and is at 20 ^$\circ$ C and 1 atm. Assuming that it only has the two diatomic gases, N₂ and O₂, the amount of kinetic energy in the gases is

A) 3.6 MJ
B) 6.1 MJ
C) 0.25 MJ
D) 0.41 MJ
E) none of the above

Question 71

A room measures 3 m $\times$ 4 m $\times$ 2 m and is at 15 ^$\circ$ C and 1 atm. Assuming that it only has the two diatomic gases, N₂ and O₂, how much heat is needed to increase the temperature to 25 ^$\circ$ C? (Ignore the loss in air as the temperature heats up.)

A) 8.4 $\times$ 10⁴ J
B) 1.3 $\times$ 10⁵ J
C) 1.7 $\times$ 10⁵ J
D) 2.1 $\times$ 10⁵ J
E) none of the above

Question 72

Five molecules of a gas have the following speeds:
200 m/s,
300 m/s,
400 m/s,
500 m/s, and
600 m/s.
The rms speed for these molecules is

A) 300 m/s
B) 344 m/s
C) 400 m/s
D) 424 m/s
E) 534 m/s

Question 73

When the temperature of an ideal gas is increased from 300 K to 400 K, the average kinetic energy of the gas molecules increases by a factor of

A) 1.15
B) 1.33
C) 1.54
D) 1.78
E) 2.47

Question 74

Use the following to answer question:
The figure shows the distribution of the molecular speeds of a gas for two different temperatures.

A) The curve labeled T₂ represents the distribution for the higher temperature molecules.
B) The point labeled "1" corresponds to the rms speed of the molecules whose temperature is T₁.
C) The point labeled "2" corresponds to the maximum speed of the molecules whose temperature is T₁.
D) The point labeled "3" corresponds to the average speed of the molecules whose temperature is T₁.
E) None of these is correct.

Question 75

A 1 L container contains O₂ gas at STP. If the diameter of the O₂ molecule is
3.75 $\times$ 10 ^-10m, the mean free path of the O₂ molecule is

A) 5.96 $\times$ 10 ^-8 m
B) 6.53 $\times$ 10 ^-8 m
C) 4.57 $\times$ 10 ^-8 m
D) 6.89 $\times$ 10 ^-8 m
E) 7.67 $\times$ 10 ^-8 m

Question 76

The isotherm that corresponds to the highest temperature is the one labeled

A) T₁
B) T₂
C) T₃
D) The isotherms correspond to the same temperature
E) none of these is correct

Question 77

Two tanks, both of volume 10 L, are connected by a valve and are thermally isolated. One tank contains 1mole of ⁴He at 280 K and the other tank contains 1 mole O₂ at 300 K. The valve is then opened and the gases allowed to mix. What is the final temperature after the gases have come to equilibrium?

A) 290 K
B) 295 K
C) 285 K
D) 293 K
E) 287 K

Question 78

Use the following to answer question:
The figure shows the distribution of the molecular speeds of a gas for two different temperatures.

A) The curve labeled T₁ represents the distribution for the higher temperature molecules.
B) The point labeled "1" corresponds to the maximum speed of the molecules whose temperature is T₁.
C) The point labeled "2" corresponds to the maximum speed of the molecules whose temperature is T₁.
D) The point labeled "3" corresponds to the average speed of the molecules whose temperature is T₁.
E) None of these is correct.

Question 79

If the rms speed of nitrogen molecules (molecular weight of N₂ is 28 g/mol) at 273 K is 492 m/s, the rms speed of oxygen molecules (molecular weight of O₂ is 32 g/mol) at the same temperature is approximately

A) 430 m/s
B) 461 m/s
C) 492 m/s
D) 526 m/s
E) 562 m/s

Question 80

The graph shows the Maxwell-Boltzmann distribution function of the number of gas molecules per unit speed range at a given temperature. The average speed, the most probable speed, and the rms speed (in this order) are most likely given by

A) x, y, z
B) z, x, y
C) y, z, x
D) y, x, z
E) z, y, x