Deck 10: Temperature and Kinetic Theory

Question 1

Some texts use the kilogram-mole rather than the gram-mole. What would be the values of the gas constant R and Avogadro's number N_A using the kg-mole?

Answer 1

R = 8.31 × 10³ J / [(kg-mole) K]
N_A = 6.02 × 10²⁶ (kg-mole)^-1

Question 2

State the equipartition theorem.

Answer 2

On average, the total internal energy of an ideal gas is divided equally among each degree of freedom its molecules possesses. Futhermore, each degree of freedom contributes 1/2 Nk_BT to the total internal energy of the gas.

Question 3

9/5 of a Fahrenheit degree is equivalent to

A) 1° C.
B) 1 K°.
C) 373.16 K.
D) 1 C°.
E) 273.16 K.

Answer 3

1 C°.

Question 4

Boyle's law and Charles' law each respectively assume what is held constant?

A) temperature, volume
B) volume, pressure
C) pressure, volume
D) temperature, pressure
E) volume, temperature

Question 5

The universal gas constant has what units?

A) molecules/mole
B) Joules
C) Joules/K
D) 1/C°
E) J/mol-K

Question 6

Avogadro's number has what units?

A) J/mol-K
B) It's dimensionless.
C) molecules/mole
D) 1/C°
E) joules/mole

Question 7

Which temperature scale never gives negative temperatures?

A) Celsius
B) Kelvin
C) Fahrenheit

Question 8

Room temperature is approximately

A) -68.° F.
B) 68. K.
C) 300.° F.
D) 300. K.
E) 68.° C.

Question 9

The Temperature of triple point of water is equivalent to which of the following?

A) 100.° C
B) 0.° F
C) 459.° F
D) 373.16 K
E) 273.16 K

Question 10

The boiling point of water is at

A) -459. K.
B) 212.° C.
C) 373.16 K.
D) 459.° F.
E) 273.16 K.

Question 11

If the pressure acting on an ideal gas at constant temperature is tripled, its volume is

A) reduced to one-half.
B) reduced to one-third.
C) increased by a factor of two.
D) increased by a factor of three.

Question 12

Both the pressure and volume of a given sample of an ideal gas double. This means that its temperature in Kelvins must

A) double.
B) remain unchanged.
C) reduce to one-half its original value.
D) reduce to one-fourth its original value.
E) quadruple.

Question 13

Which of the following would correctly convert a Fahrenheit temperature (F) to a Kelvin (K) value?

A) K = (5/9)F + 255
B) K = (5/9)F - 273
C) K = (9/5) F + 273
D) K = (5/9)(F - 32)
E) K = (9/5)(F - 32) + 273

Question 14

When the engine of your car heats up, the spark plug gap will

A) decrease at first and then increase later, so that the two effects cancel once the engine reaches operating temperature.
B) decrease.
C) increase.
D) remain unchanged.

Question 15

Aluminum has a positive coefficient of thermal expansion. Consider a round hole that has been drilled in a large sheet of aluminum. As the temperature increases and the surrounding metal expands, the hole diameter will

A) depends how much metal surrounds the hole
B) decrease.
C) remain constant.
D) increase.

Question 16

The surface water temperature on a large, deep lake is 3° C. A sensitive temperature probe is lowered several m into the lake. What temperature will the probe record?

A) a temperature less than 3° C
B) a temperature equal to 3° C
C) a temperature warmer than 3° C

Question 17

Due to the unusual thermal expansion properties of water, when a lake freezes during the winter, the water at the bottom of the lake is at ________ temperature than the water above it.

A) a lower
B) the same
C) a higher

Question 18

Water has its ________ density at 4.° C.

A) maximum
B) minimum
C) average

Question 19

Consider a flat steel plate with a hole through its center. When the plate's temperature is decreased, the hole will

A) contract only if it takes up more than half the plate's surface area.
B) expand.
C) contract.
D) expand if it takes up less than half the plate's surface area.

Question 20

A bimetallic strip, consisting of metal G on the top and metal H on the bottom, is rigidly attached to a wall at the left, as shown in Figure 10-1. The coefficient of linear thermal expansion for metal G is greater than that of metal H.

If the strip is uniformly heated, it will

A) curve downward.
B) remain horizontal, but get longer.
C) curve upward.
D) bend in the middle.

Question 21

In the equation PV = NkT, the k is known as

A) the spring (compressibility) constant.
B) compressibility.
C) Planck's constant.
D) Boltzmann's constant.
E) Avogadro's number.

Question 22

Boltzmann's constant has what units?

A) molecules/mole
B) J/K
C) Joules/mole
D) 1/C°
E) J/mol-K

Question 23

Internal energy has what units?

A) 1/C°
B) J/mol-K
C) J/K
D) molecules/mole
E) J

Question 24

The kinetic theory of gases suggests the average kinetic energy per molecule is (for a monatomic gas)

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

Question 25

Diffusion is described by

A) Graham's law.
B) Boyle's law.
C) Archimedes' law.
D) Kepler's law.
E) Charles' law.

Question 26

Gresham's Law says, at constant pressure and temperature, the diffusion rate for a gas molecule is

A) inversely proportional to mass.
B) proportional to the square root of the mass.
C) inversely proportional to the square root of the mass.
D) proportional to mass.

Question 27

In order to double the average speed of the molecules in a given sample of gas, the temperature (measured in Kelvins) must

A) quadruple.
B) double.
C) reduce to one-fourth its original value.
D) triple.
E) reduce to one-half its original value.

Question 28

An ideal gas at STP is first compressed until its volume is half the initial volume, and then it is allowed to expand until its pressure is half the initial pressure. All of this is done while holding the temperature constant. If the initial internal energy of the gas is U, the final internal energy of the gas will be

A) 2U.
B) U.
C) U/2.
D) U/3.
E) U/4.

Question 29

A sample of an ideal gas is slowly compressed to one-half its original volume with no change in temperature. What happens to the average speed of the molecules in the sample?

A) It does not change.
B) It halves.
C) It doubles.
D) cannot be determined without more information

Question 30

A sample of an ideal gas is heated and its Kelvin temperature doubles. What happens to the average speed of the molecules in the sample?

A) it is 1/ times smaller.
B) It doubles.
C) It halves.
D) it is times as large.
E) It does not change.

Question 31

Oxygen molecules are 16 times more massive than hydrogen molecules. At a given temperature, how do their average molecular speeds compare? The oxygen molecules are moving

A) at 1/4 the speed.
B) 16 times faster.
C) 4 times faster.
D) the same as the hydrogen molecules.
E) at 1/16 the speed.

Question 32

Oxygen molecules are 16 times more massive than hydrogen molecules. At a given temperature, the average molecular kinetic energy of oxygen, compared to hydrogen,

A) is less.
B) is greater.
C) cannot be determined since pressure and volume are not given.
D) is the same.

Question 33

A container is filled with a mixture of helium and oxygen gases. A thermometer in the container indicates that the temperature is 22.° C. Which gas molecules have the greater average kinetic energy?

A) It is the same for both because the temperatures are the same.
B) The oxygen molecules do because they are diatomic.
C) The oxygen molecules do because they are more massive.
D) The helium molecules do because they are less massive.
E) The helium molecules do because they are monatomic.

Question 34

What is the average separation between air molecules at STP?

Question 35

A constant pressure gas thermometer is initially at 28.° C. If the volume of gas increases by 10%, what is the final Celsius temperature?

Question 36

A container of an ideal gas at 1 atm is compressed to one-third its volume, with the temperature held constant. What is its final pressure?

Question 37

"Absolute Zero" is how many Fahrenheit degrees below freezing (water)?

Question 38

Two liters of a perfect gas are at 0° C and 1.0 atm. If the gas is nitrogen, N₂, determine:
(a) the number of mol;
(b) the number of molecules; and
(c) the mass of the gas.

Question 39

Consider a classroom 10.0 m long by 6.0 m wide by 4.0 m high at "room temperature" 20.° C and 1.0 atmosphere.
(a) How many moles of gas are contained in the room?
(b) Assuming an average molecular weight of 28, what is the mass of the room air?

Question 40

The coefficient of linear expansion for aluminum is 24. × 10^-6 K^-1. What is the coefficient in units of C °^-1?

Question 41

Ten meter long steel railroad rails are laid end to end, with no space between, on a hot day when the temperature is 115.° F. Six months later the temperature has dropped to -2.°F. How much space now exists between each rail?
[ linear expansion coef. for steel is 12. × 10^-6 C °^-1]

Question 42

Consider an aluminum rod encircling the Earth (radius 6378. km). If the linear thermal expansion coefficient of the aluminum is 24. × 10^-6 (C °)^-1, and if the temperature of the rod increases by 1.0 C°, how high off the ground would the expanded ring be (assuming uniform space all around)?

Question 43

The thermal coefficient of linear expansion of Copper is 1.7 × 10^-5 C °^-1. What is the thermal volume expansion coefficient?

Question 44

A mercury thermometer has a bulb of volume 0.100 cm³ at 10.°C. The capillary tube above the bulb has a cross-sectional area of 0.012 mm². The volume thermal expansion coefficient of mercury is 1.80 × 10^-4 K^-1. How much will the mercury rise when the temperature rises to 30.° C?

Question 45

At room temperature (20.° C) the area of a hole in a sheet of material is 5.505 cm². When heated to 830.° C the area increases by 29.0 mm².
(a) What is the thermal coefficient of linear expansion for the material?
(b) If the temperature had decreased to -76.° Fahrenheit, what would be the area of the hole?

Question 46

Given the following four speeds (in m/s) 16.0, 22.0, 36.0, and 38.0:
(a) what is the average speed?
(b) what is the rms speed?

Question 47

The temperature is such that the rms speed of nitrogen molecules is 900. m/s at 750. mm Hg pressure. If the pressure increases to 780. mm Hg while the temperature remains constant, what is the rms speed now? [Molecular weight of nitrogen molecule is 28.]

Question 48

Heat is added to an ideal gas at 20.° C. If the internal energy of the gas increases by a factor of three during this process, what is the final temperature?

Question 49

At what temperature is the average kinetic energy of an atom in helium gas equal to 6.21 × 10^-21 J?

Question 50

A mixture of helium and another gas diffuses through a porous barrier. The helium diffuses 3.16 times faster than the other type molecule. Identify the other gas.

Question 51

How many moles are there in 2.0 kg of copper? (The atomic weight of copper is 63.5 and its specific gravity is 8.9.)

Question 52

Express your body temperature (98.6°)

A) 45.5° C
B) 29.5° C
C) 66.6° C
D) 37.0° C
E) 72.6° C
F) in Celsius degrees.

Question 53

Express 45° C in °F.

A) 127° F
B) 81° F
C) 57° F
D) 113° F
E) 25° F

Question 54

A temperature change of 20 C° corresponds to a temperature change of

A) 11.1 F°.
B) 68. F°.
C) 36. F°.
D) 42. F°.
E) 20. F°.

Question 55

"Absolute Zero" is what temperature on the Celsius and Fahrenheit scales respectively?

A) 0° C, 459° F
B) -273° C, -212° F
C) -212° C, -273° F
D) -273° C, -459° F
E) -459° C, -273° F

Question 56

Which two temperature changes are equivalent?

A) -40 C°, -40 F°
B) 1 K, 1 F°
C) 1 C°, 1 K
D) 1 F°, 1 C°

Question 57

On a winter -3.° C morning, the pressure in a car tire reads 28. psi on a pressure gauge. After several hours of highway traveling, the pressure reads 35. psi. Assuming the volume remains constant and normal atmospheric pressure of 15. psi, what is the tire temperature?

A) 45° C
B) 25° C
C) 41° C
D) 55° C
E) 55° F

Question 58

A sample of a diatomic ideal gas occupies 33.6 L under standard conditions. How many moles of gas are in the sample?

A) 2.0
B) 3.0
C) 4.5
D) 1.5
E) 0.75

Question 59

The temperature of an ideal gas increases from 10° C to 300. K while remaining at constant pressure. What happens to the volume of the gas?

A) It more than doubles.
B) It decreases slightly.
C) It increases by factor of 30.
D) It decreases to one-half its original volume.
E) It increases slightly.

Question 60

Consider an ideal gas at 1.0 atmosphere in a closed container. If the temperature changes from 300. K to 450. K, the final gauge pressure will be

A) 21. psi.
B) 0.5 atm.
C) 3.0 atm.
D) 4.5 atm.
E) 1.5 atm.

Question 61

How many water molecules are there in 36. g of water? Express your answer as a multiple of Avogadro's number NA. (The molecular structure of a water molecule is H₂O.)

A) 0.020 N_A
B) 18. N_A
C) 36. N_A
D) 2.0 N_A
E) 3.0 N_A

Question 62

By how much will a slab of concrete 18. m long contract when the temperature drops from 24.° C to -16.° C? (The coefficient of linear thermal expansion for concrete is 12 × 10^-6 per degree C.)

A) 70. mm
B) 1.5 cm
C) 15. cm
D) 0.5 cm
E) 0.86 cm

Question 63

A bolt hole in a brass plate has a diameter of 1.2 cm at 20.° C. What is the diameter of the hole when the plate is heated to 220.° C? (The coefficient of linear thermal expansion for brass is 19 × 10^-6 per degree C.)

A) 1.200 cm
B) 1.190 cm
C) 1.210 cm
D) 1.195 cm
E) 1.205 cm

Question 64

The coefficient of linear expansion for brass is 19. × 10^-6 K^-1 . What is its coefficient of volume expansion?

A) 3.8 × 10^-6 K^-1
B) 5.7 × 10^-5 K^-1
C) 8 × 10^-18 K^-1
D) 57. × 10^-5 K^-1
E) 38. × 10^-6 K^-1

Question 65

The volume coefficient of thermal expansion for gasoline is 9.50 × 10^-4 per degree C. By how much does the volume of 1 L of gasoline change when the temperature rises from 20.°C to 40.°C?

A) 12. cm³
B) 6.0 cm³
C) 37. cm³
D) 24. cm³
E) 19. cm³

Question 66

How much compressional stress builds up in a thick aluminum bar held between 2 immovable walls if the temperature increases by 20. C°?
( $\alpha$ = 24. × 10^-6 C^-1, Y = 7 × 10¹⁰ N/m²)

A) 34. × 10⁷ N/m²
B) 34. × 10⁸ N/m²
C) 34. × 10⁶ N/m²
D) 34. × 10⁴ N/m²
E) 34. × 10⁵ N/m²

Question 67

A confined gas has an average energy/molecule of 60. meV. If the pressure is tripled and the volume is reduced by a factor of 3, what now is the average energy?

A) 0.18 eV
B) 0.10 eV
C) 0.03 eV
D) 0.06 eV
E) 0.02 eV

Question 68

At which of the following temperatures would we expect gas molecules to have half the energy that they have at 100.° C?

A) -86.° C
B) 93. K
C) 323. K
D) -56.° C
E) 50.° C