Deck 13: Temperature and Kinetic Theory

Question 1

Choose the one alternative that best completes the statement or answers the question.
A sample of an ideal gas is heated and its Kelvin temperature doubles. If the root-mean-square speed of its molecules was originally v, what is the new root-mean-square speed?

A) $4 v$
B) $v / \sqrt { 2 }$
C) $v \sqrt { 2 }$
D) $v / 4$
E) $2 v$

Answer 1

C

Question 2

Choose the one alternative that best completes the statement or answers the question.
Consider a flat steel plate with a hole through its center as shown in the figure. When the temperature of the plate is increased, the hole will

A) always expand with the plate.
B) contract if it takes up less than half the plate's surface area.
C) remain the same size as the plate expands around it.
D) expand only if it takes up more than half the plate's surface area.
E) always contract as the plate expands into it.

Answer 2

always expand with the plate.

Question 3

Choose the one alternative that best completes the statement or answers the question.
Nitrogen boils at $- 196 ^ { \circ } \mathrm { C }$ What is the corresponding temperature in the Fahrenheit scale?

A) $- 321 ^ { \circ } \mathrm { F }$
B) $- 196 ^ { \circ } \mathrm { F }$
C) $- 346 ^ { \circ } \mathrm { F }$
D) $- 315 ^ { \circ } \mathrm { F }$
E) $- 290 ^ { \circ } \mathrm { F }$

Answer 3

A

Question 4

Choose the one alternative that best completes the statement or answers the question.
As shown in the figure, 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. 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) remain horizontal, but get longer.
B) bend in the middle.
C) curve upward.
D) remain horizontal, but get shorter.
E) curve downward.

Question 5

Choose the one alternative that best completes the statement or answers the question.
Oxygen condenses into a liquid at approximately 90 K. What temperature, in degrees Fahrenheit, does this correspond to?

A) $- 265 ^ { \circ } \mathrm { F }$
B) $- 217 ^ { \circ } \mathrm { F }$
C) $- 297 ^ { \circ } \mathrm { F }$
D) $- 193 ^ { \circ } \mathrm { F }$

Question 6

Choose the one alternative that best completes the statement or answers the question.
At what, if any, temperature are the numerical readings on the Fahrenheit and Celsius scales the same?

A) $- 60 ^ { \circ }$
B) $- 40 ^ { \circ }$
C) $- 50 ^ { \circ }$
D) $- 30 ^ { \circ }$
E) They can never read the same because they are based on different zeroes.

Question 7

Choose the one alternative that best completes the statement or answers the question.
The root-mean-square speed of the molecules of an ideal gas is v. The gas is now slowly compressed to one-half its original volume with no change in temperature. What is the
Root-mean-square speed of the molecules now?

A) $v$
B) $2 v$
C) $v / \sqrt { 2 }$
D) $v / 2$
E) $4 v$

Question 8

Choose the one alternative that best completes the statement or answers the question.
A temperature change of $20 \mathrm { C } ^ { \circ }$ corresponds to a Fahrenheit temperature change of

A) $68 \mathrm {~F} ^ { \circ }$
B) $11 \mathrm {~F} ^ { \circ } .$
C) $18 \mathrm {~F} ^ { \circ } \text {. }$
D) $36 \mathrm {~F} ^ { \circ } \text {. }$

Question 9

Choose the one alternative that best completes the statement or answers the question.
The absolute temperature of a gas is T. In order to double the rms speed of its molecules, what should be the new absolute temperature?

A) 2T
B) 4T
C) $T \sqrt { 2 }$
D) 16T
E) 8T

Question 10

Choose the one alternative that best completes the statement or answers the question.
Two containers of equal volume each hold samples of the same ideal gas. Container A has twice as many molecules as container B . If the gas pressure is the same in the two containers, the correct statement regarding the absolute temperatures $T _ { A } \text { and } T _ { B }$ in containers A and B, respectively, is

A) $T _ { A } = T_ {B}$
B) $T _ { A } = \frac { 1 } { 2 } T _ { B }$
C) $T _ { \mathbf { A } } = \frac { 1 } { \sqrt { 2 } } T _ { \mathrm { B } }$
D) $T _ { \mathbf { A } } = 2 T _ { \mathbf { B } }$
E) $T _ { A } = \frac { 1 } { 4 } T _ { B }$

Question 11

Choose the one alternative that best completes the statement or answers the question.
Express a body temperature 98.6°F in Celsius degrees.

A) $66.6 ^ { \circ } \mathrm { C }$
B) $72.6 ^ { \circ } \mathrm { C }$
C) $37.0 ^ { \circ } \mathrm { C }$
D) $45.5 ^ { \circ } \mathrm { C }$

Question 12

Choose the one alternative that best completes the statement or answers the question.
Express $- 40 ^ { \circ } \mathrm { C } \text { in } { } ^ { \circ } \mathrm { F } \text {. }$

A) $4.4 ^ { \circ } \mathrm { F }$
B) $- 54 ^ { \circ } \mathrm { F }$
C) $- 72 ^ { \circ } \mathrm { F }$
D) $- 40 ^ { \circ } \mathrm { F }$

Question 13

Choose the one alternative that best completes the statement or answers the question.
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) four times faster than the hydrogen molecules.
B) at 1/4 the speed of the hydrogen molecules.
C) at 1/16 the speed of the hydrogen molecules.
D) sixteen times faster than the hydrogen molecules.
E) at $1 / \sqrt { 2 }$ the speed of the hydrogen molecules.

Question 14

Choose the one alternative that best completes the statement or answers the question.
Which two temperature changes are equivalent?

A) $1 C ^ { \circ } = 1 K$
B) $1 F ^ { \circ } = 1 C ^ { \circ }$
C) $1 \mathrm {~K} = 1 \mathrm {~F} ^ { \circ }$
D) none of the above

Question 15

Write the word or phrase that best completes each statement or answers the question.
What is absolute zero on the (a) Celsius scale and (b) on the Fahrenheit scale?

Question 16

Choose the one alternative that best completes the statement or answers the question.
The temperature in your classroom is closest to

A) 68 K
B) $50 ^ { \circ } \mathrm { C }$
C) $68 ^ { \circ } \mathrm { C }$
D) 295 K

Question 17

Choose the one alternative that best completes the statement or answers the question.
An ideal gas is held in a container of volume V at pressure p . The rms speed of a gas molecule under these conditions is $v$ If now the volume and pressure are changed to 2 V and 2 p , the rms speed of a molecule will be

A) $4 v$
B)
C) $v / 2$
D) $2 v$
E) $v / 4$

Question 18

Choose the one alternative that best completes the statement or answers the question.
Consider two equal-volume flasks of gas at the same temperature and pressure. One gas, oxygen, has a molecular mass of 32 . The other gas, nitrogen, has a molecular mass of 28 . What is the ratio of the number of oxygen molecules to the number of nitrogen molecules in these flasks?

A) $\sqrt { \frac { 32 } { 28 } }$
B) $\sqrt { \frac { 28 } { 32 } }$
C) $\frac { 32 } { 38 }$
D) $\frac { 28 } { 32 }$
E) $\frac { 1 } { 1 }$

Question 19

Choose the one alternative that best completes the statement or answers the question.
The coefficient of linear expansion for aluminum is $1.8 \times 10 ^ { - 6 } \mathrm {~K} - 1$
What is its coefficient of volume expansion?

A) $5.4 \times 10 ^ { - 6 } \mathrm {~K} ^ { - 1 }$
B) $9.0 \times 10 ^ { - 6 } \mathrm {~K} ^ { - 1 }$
C) $3.6 \times 10 ^ { - 6 } K - 1$
D) $5.8 \times 10 ^ { - 18 } K - 1$
E) $0.60 \times 10 ^ { - 6 } \mathrm {~K} ^ { - 1 }$

Question 20

Choose the one alternative that best completes the statement or answers the question.
The temperature changes from $35 ^ { \circ } \mathrm { F }$ during the night to $75 ^ { \circ } \mathrm { F }$ during the day. What is the temperature change on the Celsius scale?

A) $32 \mathrm { C } ^ { \circ }$
B) $22 \mathrm { C } ^ { \circ }$
C) $72 \mathrm { C } ^ { \circ }$
D) $40 C ^ { \circ }$

Question 21

Choose the one alternative that best completes the statement or answers the question.
A mercury thermometer has a glass bulb of interior volume $0.100 \mathrm {~cm} ^ { 3 } \text { at } 10 ^ { \circ } \mathrm { C }$ The glass capillary tube above the bulb has an inner cross-sectional area of $0.012 \mathrm {~mm} ^ { 2 }$ . The coefficient of volume expansion of mercury is $1.8 \times 10 ^ { - 4 } K ^ { - 1 }$ . If the expansion of the glass is negligible, how much will the mercury rise in the capillary tube when the temperature rises from $5 ^ { \circ } \mathrm { C } \text { to } 35 ^ { \circ } \mathrm { C }$ if the bulb was full at $5 ^ { \circ } \mathrm { C } ?$ ?

A) 4.5 mm
B) 0.45 mm
C) 45 cm
D) 45 mm

Question 22

Choose the one alternative that best completes the statement or answers the question.
An aluminum rod 17.400 cm long at $20 ^ { \circ } \mathrm { C }$ is heated to $100 ^ { \circ } \mathrm { C }$ What is its new length? Aluminum has a linear expansion coefficient of $25 \times 10 ^ { - 6 } K ^ { - 1 }$

A) 0.0348 cm
B) 0.348 cm
C) 17.435 cm
D) 17.365 cm

Question 23

Choose the one alternative that best completes the statement or answers the question.
The coefficient of linear expansion of aluminum is $24.0 \times 10 ^ { - 6 } \mathrm {~K} ^ { - 1 }$ and the density of aluminum at $0 ^ { \circ } \mathrm { C } \text { is } 2.70 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 } \text {. }$ What is the density of aluminum at $300 ^ { \circ } \mathrm { C } \text { ? }$

A) $3.93 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$
B) $2.70 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$
C) $2.67 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$
D) $2.73 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$
E) $2.64 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Question 24

Choose the one alternative that best completes the statement or answers the question.
The density of water at $0 ^ { \circ } \mathrm { C }$ is $999.84 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ and at $4 ^ { \circ } \mathrm { C }$ it is $999.96 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ A 1.0-L container, full to
the brim with water at $4.0 ^ { \circ } \mathrm { C }$ is placed in the refrigerator. By the time that the temperature of the
water reaches $0.0 ^ { \circ } \mathrm { C }$ what volume of water has spilled from the container, assuming that the
contraction of the container is negligible?

A) $1.1 \times 10 ^ { - 7 } \mathrm {~m} ^ { 3 }$
B) $14 \times 10 ^ { - 7 } \mathrm {~m} ^ { 3 }$
C) $1.5 \times 10 ^ { - 7 } \mathrm {~m} ^ { 3 }$
D) $1.2 \times 10 ^ { - 7 } \mathrm {~m} ^ { 3 }$
E) $1.3 \times 10 ^ { - 7 } \mathrm {~m} ^ { 3 }$

Question 25

Choose the one alternative that best completes the statement or answers the question.
The weather outside is frightful. The temperature is $- 22 ^ { \circ } \mathrm { F }$ What is the corresponding temperature in the Celsius scale?

A) $- 20 ^ { \circ } \mathrm { C }$
B) $- 35 ^ { \circ } \mathrm { C }$
C) $- 30 ^ { \circ } \mathrm { C }$
D) $- 22 ^ { \circ } \mathrm { C }$
E) $- 12 ^ { \circ } \mathrm { C }$

Question 26

Choose the one alternative that best completes the statement or answers the question.
A quantity of mercury occupies $400.0 \mathrm {~cm} ^ { 3 } \text { at } 0 ^ { \circ } \mathrm { C }$ What volume will it occupy when heated to $50 ^ { \circ } \mathrm { C } ?$ Mercury has a volume expansion coefficient of $180 \times 10 ^ { - 6 } \mathrm {~K} ^ { - 1 }$

A) $450 \mathrm {~cm} ^ { 3 }$
B) $401.8 \mathrm {~cm} ^ { 3 }$
C) $409.7 \mathrm {~cm} ^ { 3 }$
D) $403.6 \mathrm {~cm} ^ { 3 }$

Question 27

Choose the one alternative that best completes the statement or answers the question.
A steel bridge is 1000 m long at $- 20 ^ { \circ } \mathrm { C }$ in winter. What is the change in length when the temperature rises to $40 ^ { \circ } \mathrm { C }$ in summer? The average coefficient of linear expansion of this steel is $11$ $\times 10 ^ { - 6 } K - 1$

A) 0.33 m
B) 0.44 m
C) 0.66 m
D) 0.55 m

Question 28

Choose the one alternative that best completes the statement or answers the question.
The coefficient of linear expansion of aluminum is $24 \times 10 ^ { - 6 } \mathrm {~K} ^ { - 1 }$ \quad and the coefficient of volume
expansion of olive oil is $0.68 \times 10 ^ { - 3 } \mathrm {~K} ^ { - 1 }$ . A novice cook, in preparation of some pesto, fills a 1.00-L
aluminum pot to the brim and heats the oil and the pot from an initial temperature of $15 ^ { \circ } \mathrm { C }$ to
$190 ^ { \circ } \mathrm { C }$ To his consternation some olive oil spills over the top. How much?

A) 0.14 L
B) 0.12 L
C) 0.13 L
D) 0.11 L
E) 0.15 L

Question 29

Choose the one alternative that best completes the statement or answers the question.
The coefficient of linear expansion of copper is $17 \times 10 ^ { - 6 } K - 1$ A sheet of copper has a round hole with a radius of 3.0 m cut out of it. If the sheet is heated and undergoes a change in temperature of 80 K, what is the change in the radius of the hole?

A) It decreases by 4.1 mm
B) It decreases by 8.2 mm
C) It does not change.
D) It increases by 4.1 mm
E) It increases by 8.2 mm

Question 30

Choose the one alternative that best completes the statement or answers the question.
The coefficient of linear expansion of copper is $17 \times 10 ^ { - 6 } K ^ { - 1 }$ A block of copper 30 cm wide, 45 cm Iong, and 10 cm thick is heated from $0 ^ { \circ } \mathrm { C } \text { to } 100 ^ { \circ } \mathrm { C }$
What is the change in the volume of the block?

A) $6.9 \times 10 ^ { - 5 } \mathrm {~m} ^ { 3 }$
B) $4.6 \times 10 ^ { - 5 } \mathrm {~m} ^ { 3 }$
C) $14 \times 10 ^ { - 5 } m ^ { 3 }$
D) $2.3 \times 10 ^ { - 5 } \mathrm {~m} ^ { 3 }$
E) $5.2 \times 10 ^ { - 5 } \mathrm {~m} ^ { 3 }$

Question 31

Choose the one alternative that best completes the statement or answers the question.
A large vat contains 1.000 L of water at $20 ^ { \circ } \mathrm { C }$ What volume will this water occupy when it is heated up to $80 ^ { \circ } \mathrm { C } ?$ Water has a volume expansion coefficient of $210 \times 10 ^ { - 6 } K ^ { - 1 }$

A) 0.987 L
B) 1.600 L
C) 1.013 L
D) 0.9987 L

Question 32

Choose the one alternative that best completes the statement or answers the question.
By what length will a slab of concrete that is originally 18 m long contract when the temperature drops from $24 ^ { \circ } \mathrm { C } \text { to } - 16 ^ { \circ } \mathrm { C } ?$
The coefficient of linear thermal expansion for this concrete is $1.0 \times$ $10^{ - 5} \mathrm {~K} ^ { - 1 }$

A) 1.5 cm
B) 1.2 cm
C) 0.50 cm
D) 0.72 cm

Question 33

Choose the one alternative that best completes the statement or answers the question.
For the mercury in a thermometer to expand from $4.00 \mathrm {~cm} ^ { 3 } \text { to } 4.10 \mathrm {~cm} ^ { 3 }$ what change in temperature is necessary? The mercury has a volume expansion coefficient of $1.80 \times 10 ^ { - 4 } K ^ { - 1 }$

A) $140 C ^ { \circ }$
B) $400 \mathrm { C } ^ { \circ }$
C) $8.2 \mathrm { C } ^ { \circ }$
D) $14 C ^ { \circ }$

Question 34

Choose the one alternative that best completes the statement or answers the question.
The coefficient of linear expansion of copper is $17 \times 10 ^ { - 6 } \mathrm {~K} ^ { - 1 }$ and that of steel is $12 \times 10 ^ { - 6 } K ^ { - 1 }$ At $12 ^ { \circ } \mathrm { C }$ a steel rod has a diameter of 2.540 cm and a copper pipe has a diameter of 2.536 cm. If they
are heated together to a higher temperature, which one of the following quantities is closest to the
common temperature at which the steel rod will fit snugly in the copper pipe?

A) $350 ^ { \circ } \mathrm { C }$
B) $330 ^ { \circ } \mathrm { C }$
C) $340 ^ { \circ } \mathrm { C }$
D) $310 ^ { \circ } \mathrm { C }$
E) $380 ^ { \circ } \mathrm { C }$

Question 35

Choose the one alternative that best completes the statement or answers the question.
A hole in a brass plate has a diameter of 1.200 cm at $20 ^ { \circ } \mathrm { C }$ What is the diameter of the hole when the plate is heated to $220 ^ { \circ } \mathrm { C } ?$
The coefficient of linear thermal expansion for brass is $19 \times 10 ^ { - 6 } K ^ { - 1 }$

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

Question 36

Choose the one alternative that best completes the statement or answers the question.
Suppose that a rigid aluminum wire were to be strung out in a loop that just fits snugly around the equator (assuming a perfectly spherical Earth with a radius of $\left. 6.37 \times 10 ^ { 6 } \mathrm {~m} \right)$
If the temperature of the wire is increased by $0.50 ^ { \circ } \mathrm { C }$ and the increase in length is distributed equally over the entire length, how far off the ground will the wire loop be if it remained centered on the earth? The coefficient of linear expansion of aluminum is $24 \times 10 ^ { - 6 } K ^ { - 1 }$

A) 76 mm
B) 76 m
C) 7.6 mm
D) 76 cm
E) 760 m

Question 37

Choose the one alternative that best completes the statement or answers the question.
The volume coefficient of thermal expansion for gasoline is $950 \times 10 ^ { - 6 } K ^ { - 1 }$ By how many cubic centimeters does the volume of 1.00 L of gasoline change when the temperature rises from $30 ^ { \circ } \mathrm { C }$ to $50 ^ { \circ } \mathrm { C } ?$

A) $37 \mathrm {~cm} ^ { 3 }$
B) $19 \mathrm {~cm} ^ { 3 }$
C) $12 \mathrm {~cm} ^ { 3 }$
D) $6.0 \mathrm {~cm} ^ { 3 }$

Question 38

Choose the one alternative that best completes the statement or answers the question.
The coefficient of linear expansion of copper is $17 \times 10 ^ { - 6 } K^{ - 1}$ and that of steel is $12 \times 10 ^ { - 6 } K^{ - 1}$ At $12 ^ { \circ } \mathrm { C }$ a steel rod has a diameter of 2.540 cm and a copper pipe has a diameter of 2.536 cm. Which one of the following quantities is closest to the temperature to which the copper pipe must be heated in order for the unheated steel rod to fit snugly in the copper pipe?

A) $143 ^ { \circ } \mathrm { C }$
B) $93 ^ { \circ } \mathrm { C }$
C) $53 ^ { \circ } \mathrm { C }$
D) $105 ^ { \circ } \mathrm { C }$
E) $81 ^ { \circ } \mathrm { C }$

Question 39

Choose the one alternative that best completes the statement or answers the question.
The coefficient of volume expansion of a certain olive oil is $0.68 \times 10 ^ { - 3 } \mathrm {~K}^{ - 1}$
A 1.0 -L glass beaker is filled to the brim with olive oil at room temperature. The beaker is placed on a range and the temperature of the oil and beaker increases by $25 \mathrm { C } ^ { \circ }$ As a result, 0.0167 L of olive oil spills over the top of the beaker. Which of the following values is closest to the coefficient of linear expansion of the glass from which the beaker is made?

A) $4 \times 10 ^ { - 6 } K ^ { - 1 }$
B) $1 \times 10 ^ { - 5 } K ^ { - 1 }$
C) $1 \times 10 ^ { - 6 } K ^{- 1}$
D) $2 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 }$
E) $3 \times 10 ^ { - 5 } K ^{- 1}$

Question 40

Choose the one alternative that best completes the statement or answers the question.
Platinum melts at $3215 ^ { \circ } \mathrm { F }$ What is the corresponding temperature in the Kelvin scale?

A) 2135 K
B) 3215 K
C) 2041 K
D) 2296 K
E) 2207 K

Question 41

Choose the one alternative that best completes the statement or answers the question.
An ideal gas has a pressure of 2.5 atm, a volume of 1.0 L at a temperature of $30 ^ { \circ } \mathrm { C }$ How many molecules are there in this gas? $\left( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } , 1.00 \mathrm {~atm} = 101 \mathrm { kPa } , N _ { \mathrm { A } } = 6.022 \times 10 ^ { 23 } \right)$

A) $6.1 \times 10 ^ { 23 }$
B) $2.3 \times 10 ^ { 23 }$
C) $2.4 \times 10^{22}$
D) $6.0 \times 10^{22}$

Question 42

Choose the one alternative that best completes the statement or answers the question.
A laboratory vacuum pump can reduce the pressure in a chamber to $1.0 \times 10 ^ { - 7 } \mathrm {~Pa}$ If the volume of the chamber is $0.500 m ^ { 3 }$ and the temperature is $27 ^ { \circ } \mathrm { C }$ how many molecules are left inside chamber? $\left( N _ { \mathrm { A } } = 6.022 \times 10 ^ { 23 } \mathrm { molecules } / \mathrm { mol } , R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } \right)$

A) $2.4 \times 10 ^ { 13 }$
B) $1.2 \times 10 ^ { 14 }$
C) $1.2 \times 10^{13}$
D) $1.2 \times 10^{12}$
E) $2.4 \times 10 ^ { 12 }$

Question 43

Choose the one alternative that best completes the statement or answers the question.
A 20.0-L pressure vessel holds 2.00 mol of oxygen at $30 ^ { \circ } \mathrm { C }$ What is the pressure inside the vessel? $( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } )$

A) 1.01 MPa
B) 252 kPa
C) 2.52 MPa
D) 101 kPa
E) 101 Pa

Question 44

Choose the one alternative that best completes the statement or answers the question.
A certain automobile tire has a volume of $0.0185 \mathrm {~m} ^ { 3 }$ If the absolute (or total) pressure in the tire is 500 kPa and the temperature is 298 K, how many molecules are there inside the tire? $( R = 8.31$ $\left. \mathrm { J } / \mathrm { mol } \cdot \mathrm { K } , N _ { \mathrm { A } } = 6.022 \times 10 ^ { 23 } \mathrm { molecules } / \mathrm { mol } \right)$

A) $3.25 \times 10^{24} \text { molecules }$
B) $3.25 \times 10 ^ { 23 } \text { molecules }$
C) $2.25 \times 10^{23} \text { molecules }$
D) $3.25 \times 10^{25} \text { molecules }$
E) $2.25 \times 10^{24} \text { molecules }$

Question 45

Write the word or phrase that best completes each statement or answers the question.
A jar holds 2.0 L of ideal nitrogen gas, $\mathrm { N } _ { 2 }$ at STP. The atomic mass of nitrogen is 14.0 g/mol, the ideal gas constant is $R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K }$ Avogadro's number is $N _ { \mathrm { A } } = 6.022 \times$ $10^{23} \text { molecules/mol, }$ and 1.00 atm=101 kPa
(a) How many moles of nitrogen are in the jar?
(b) How many nitrogen molecules are in the jar?
(c) What is the mass of the nitrogen in the jar?

Question 46

Choose the one alternative that best completes the statement or answers the question.
Your lungs hold 4.2 L of air at a temperature of $27 ^ { \circ } \mathrm { C }$ and a pressure of 101.3 kPa. How many moles of air do your lungs hold? $( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } )$

A) 0.17 moles
B) 0.15 moles
C) 0.19 moles
D) 0.21 moles
E) 0.23 moles

Question 47

Choose the one alternative that best completes the statement or answers the question.
A brass rod is 69.5 cm long and an aluminum rod is 49.3 cm long when both rods are at an initial temperature of $0 ^ { \circ } \mathrm { C }$ The rods are placed in line with a gap of 1.2 cm between them, as shown in the figure. The distance between the far ends of the rods is maintained at 120.0 cm throughout. The temperature of both rods is raised equally until they are barely in contact. At what temperature does contact occur? The coefficients of linear expansion of brass and aluminum are $2.0 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 } \text { (brass) and } 2.4 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 } \text { (aluminum). }$

A) $510 ^ { \circ } \mathrm { C }$
B) $470 ^ { \circ } \mathrm { C }$
C) $440 ^ { \circ } \mathrm { C }$
D) $490 ^ { \circ } \mathrm { C }$
E) $420 ^ { \circ } \mathrm { C }$

Question 48

Write the word or phrase that best completes each statement or answers the question.
If a certain sample of an ideal gas has a temperature of $104 ^ { \circ } \mathrm { C }$ and exerts a pressure of $2.3$ $\times 10 ^ { 4 } \mathrm {~Pa}$ on the walls of its container, how many gas molecules are present in each cubic centimeter of volume? The ideal gas constant is R=8.31 J/mol x K and Avogadro's number is $N _ { A } = 6.022 \times 10^{23}$ molecules/mol.

Question 49

Write the word or phrase that best completes each statement or answers the question.
Originally 2.00 mol of gas are at STP. If the temperature changes to $47.0 ^ { \circ } \mathrm { C }$ and the pressure decreases to half of what it was, how many liters do the two moles now occupy? (1 atm=101 kPa, R=8.31 J/mol . K)

Question 50

Write the word or phrase that best completes each statement or answers the question.
How many molecules are in (a) $1.0 \mathrm {~cm} ^ { 3 }$ of air at STP and (b) $1.0 \mathrm {~cm} ^ { 3 }$ of helium at STP? (R
$\left. = 8.31 \mathrm {~J} / \mathrm { mol } . \mathrm { K } , N _ { \mathrm { A } } = 6.022 \times 10 ^ { 23 } \mathrm { molecules } / \mathrm { mol } \right)$

Question 51

Choose the one alternative that best completes the statement or answers the question.
A steel pipe 36.0 m long, installed when the temperature was $15 ^ { \circ } \mathrm { C } ,$ is used to transport superheated steam at a temperature of $155 ^ { \circ } \mathrm { C }$ Steel's coefficient of Iinear expansion is $1.2 \times 10 ^ { - 5 } K ^{- 1}$
The pipe is allowed to expand freely when the steam is transported. What is the increase in the length of the pipe when it is used with the superheated steam?

A) 60 mm
B) 67 mm
C) 57 mm
D) 54 mm
E) 64 mm

Question 52

Choose the one alternative that best completes the statement or answers the question.
A balloon originally has a volume of $1.0 \mathrm {~m} ^ { 3 }$ when the gas in it is at $20 ^ { \circ } \mathrm { C }$ and under a pressure of 1.0 atm. As it rises in the earth's atmosphere, its volume expands. What will be its new volume if its final temperature and pressure are $- 40 ^ { \circ } \mathrm { C }$ and 0.10 atm ?

A) $6.0 \mathrm {~m} ^ { 3 }$
B) $2.0 \mathrm {~m} ^ { 3 }$
C) $4.0 \mathrm {~m} ^ { 3 }$
D) $8.0 \mathrm {~m} ^ { 3 }$

Question 53

Write the word or phrase that best completes each statement or answers the question.
A solid object has a volume density $\rho O$ at a temperature of 315K. The coefficient of volume expansion for the material of which it is made is $7.00 \times 10 ^ { - 5 } K ^ { - 1 }$ What will be its density (in terms of $\rho 0$ at a temperature of 425 K, assuming that it does not melt and that its thermal properties do not change with temperature?

Question 54

Choose the one alternative that best completes the statement or answers the question.
An ideal gas occupies $6.00 \times 10 ^ { 2 } \mathrm {~cm} ^ { 3 } \text { at } 20 ^ { \circ } \mathrm { C }$ At what temperature will it occupy $1.20 \times 10 ^ { 3 } \mathrm {~cm} ^ { 3 }$ if the pressure is held constant?

A) $100 ^ { \circ } \mathrm { C }$
B) $313 ^ { \circ } \mathrm { C }$
C) $10 ^ { \circ } \mathrm { C }$
D) $40 ^ { \circ } \mathrm { C }$

Question 55

Choose the one alternative that best completes the statement or answers the question.
On a cold day, you take in 4.2 L of air into your lungs at a temperature of $0 ^ { \circ } \mathrm { C }$ If you hold your breath until the temperature of the air in your lungs reaches $37 ^ { \circ } \mathrm { C }$ what is the volume of the air in your lungs at that point, assuming the pressure does not change?

A) 5.0 L
B) 4.2 L
C) 4.8 L
D) 4.6 L
E) 4.4 L

Question 56

Choose the one alternative that best completes the statement or answers the question.
A glass flask has a volume of 500 mL at a temperature of $20 ^ { \circ } \mathrm { C }$ The flask contains 492 mL of mercury at an equilibrium temperature of $20 ^ { \circ } \mathrm { C }$ The temperature is raised until the mercury reaches the 500 mL reference mark. At what temperature does this occur? The coefficients of volume expansion of mercury and glass are $18 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 }$ (mercury) and $2.0 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 } \text { (glass) }$

A) $110 ^ { \circ } \mathrm { C }$
B) $100 ^ { \circ } \mathrm { C }$
C) $140 ^ { \circ } \mathrm { C }$
D) $130 ^ { \circ } \mathrm { C }$
E) $120 ^ { \circ } \mathrm { C }$

Question 57

Choose the one alternative that best completes the statement or answers the question.
An aluminum rod is 10.0 cm long and a steel rod is 80.0 cm long when both rods are at a temperature of $15 ^ { \circ } \mathrm { C }$ Both rods have the same diameter. The rods are now joined end-to-end to form a rod 90.0 cm long. If the temperature is now raised from $15 ^ { \circ } \mathrm { C } \text { to } 90 ^ { \circ } \mathrm { C }$ what is the increase in the length of the joined rod? The coefficient of linear expansion of aluminum is $2.4 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 }$ and that of steel is $1.2 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 }$

A) 0.90 mm
B) 0.81 mm
C) 0.63 mm
D) 0.72 mm
E) 0.99 mm

Question 58

Choose the one alternative that best completes the statement or answers the question.
A weather balloon containing $2.0 \mathrm {~m} ^ { 3 }$ of hydrogen gas rises from a location at which the temperature is $22 ^ { \circ } \mathrm { C }$ and the pressure is 101 kPa to a location where the temperature is $- 39 ^ { \circ } \mathrm { C }$ and the pressure is 20 kPa. If the balloon is free to expand so that the pressure of the gas inside is equal to the ambient pressure, what is the new volume of the balloon?

A) $8.0 \mathrm {~m} ^ { 3 }$
B) $4.0 \mathrm {~m} ^ { 3 }$
C) $12 m ^ { 3 }$
D) $10 m ^ { 3 }$
E) $6.0 \mathrm {~m} ^ { 3 }$

Question 59

Choose the one alternative that best completes the statement or answers the question.
How many moles are there in 2.00 kg of copper? The atomic weight of copper is 63.5 g/mol and its density is $8.90 \mathrm {~g} / \mathrm { cm } ^ { 3 }$

A) 31.5
B) 51.3
C) 53.1
D) 15.3

Question 60

Choose the one alternative that best completes the statement or answers the question.
A car starts out when the air temperature is 288 K and the absolute (total) air pressure in the tires is 500 kPa. After driving a while, the temperature of the air in the tires increases to 298 K. What is the pressure in the tires at that point, assuming their volume does not change?

A) 532 kPa
B) 129 kPa
C) 517 kPa
D) 507 kPa
E) 483 kPa

Question 61

Choose the one alternative that best completes the statement or answers the question.
A sealed cylinder fitted with a movable piston contains ideal gas at $27 ^ { \circ } \mathrm { C }$ pressure $0.500 \times 10 ^ { 5 } \mathrm {~Pa}$ and volume $1.25 \mathrm {~m} ^ { 3 }$ What will be the final temperature if the gas is compressed to $0.800 \mathrm {~m} ^ { 3 }$ the pressure rises to $0.820 \times 10 ^ { 5 } \mathrm {~Pa} ?$

A) $42 ^ { \circ } \mathrm { C }$
B) $150 ^ { \circ } \mathrm { C }$
C) $250 ^ { \circ } \mathrm { C }$
D) $130 ^ { \circ } \mathrm { C }$
E) $68 ^ { \circ } \mathrm { C }$

Question 62

Choose the one alternative that best completes the statement or answers the question.
A sealed container holds 0.020 moles of ideal nitrogen $\left( \mathrm { N } _ { 2 } \right)$ gas, at a pressure of 1.5 atm and a temperature of 290 K. The atomic mass of nitrogen is 14.0 g/mol. What is the average translational kinetic energy of a nitrogen molecule? The Boltzmann constant is $1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K }$

A) $4.0 \times 10 ^ { 21 } \mathrm {~J}$
B) $8.0 \times 10 ^ { 21 } \mathrm {~J}$
C) $12 \times 10^{21} \mathrm {~J}$
D) $6.0 \times 10^{21} \mathrm {~J}$
E) $10 \times 10^{21} \mathrm {~J}$

Question 63

Choose the one alternative that best completes the statement or answers the question.
The rms speed of a certain sample of carbon dioxide molecules, with a molecular weight of 44.0 g/mole, is 396 m/s. What is the rms speed of water vapor molecules, with a molecular weight of 18.0 g/mol, at the same temperature as the carbon dioxide?

A) 253 m/s
B) 619 m/s
C) 506 m/s
D) 421 m/s
E) 387 m/s

Question 64

Choose the one alternative that best completes the statement or answers the question.
What is the average translational kinetic energy of a nitrogen molecule in the air in a room in which the air temperature is $17 ^ { \circ } \mathrm { C } ?$ The Boltzmann constant is $1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K }$

A) $6.01 \times 10 ^ { - 21 } \mathrm {~J}$
B) $7.00 \times 10 ^ { - 21 } \mathrm {~J}$
C) $5.00 \times 10 ^ { - 21 } \mathrm {~J}$
D) $9.00 \times 10 ^ { - 21 } \mathrm {~J}$
E) $4.00 \times 10 ^ { - 21 } \mathrm {~J}$

Question 65

Write the word or phrase that best completes each statement or answers the question.
A flask contains a mixture of argon and neon gases at a stabilized temperature. The root-mean-square speed of the argon gas is determined to be 1.21 km/s. What is the root-mean-square speed of the neon gas? The atomic mass of argon is 39.95 g/mol, and that of neon is 20.18 g/mol.

Question 66

Choose the one alternative that best completes the statement or answers the question.
A 4.2-L flask of ideal neon gas (which is monatomic) is at a pressure of 3.3 atm and a temperature of 450 K. The atomic mass of neon is 20.2 g/mol. How many neon atoms are in the flask? $( R = 8.31$ $\left. \mathrm { J } / \mathrm { mol } \cdot \mathrm { K } , 1 \mathrm {~atm} = 101 \mathrm { kPa } , N _ { \mathrm { A } } = 6.022 \times 10 ^ { 23 } \mathrm { molecules } / \mathrm { mol } \right)$

A) $2.3 \times 10^{22}$
B) $6.9 \times 10^{22}$
C) $2.3 \times 10 ^ { 25 }$
D) $6.9 \times 10^{23}$
E) $2.3 \times 10 ^ { 23 }$

Question 67

Choose the one alternative that best completes the statement or answers the question.
The molecular weight of nitrogen, $\mathrm { N } _ { 2 }$ is 28 g/mol. What is the rms speed of nitrogen molecules in a cooler at $8.0 ^ { \circ } \mathrm { C } ?$ The Boltzmann constant is $1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K } \text { and } N _ { \mathrm { A } } = 6.022 \times 10 ^ { 23 }$ molecules/mol.

A) 550 m/s
B) 650 m/s
C) 500 m/s
D) 600 m/s
E) 450 m/s

Question 68

Choose the one alternative that best completes the statement or answers the question.
A quantity of an ideal gas is kept in a rigid container of constant volume. If the gas is originally at a temperature of $19 ^ { \circ } \mathrm { C }$ at what temperature will the pressure of the gas double from its original value?

A) $273 ^ { \circ } \mathrm { C }$
B) $91 ^ { \circ } \mathrm { C }$
C) $311 ^ { \circ } \mathrm { C }$
D) $122 ^ { \circ } \mathrm { C }$
E) $38 ^ { \circ } \mathrm { C }$

Question 69

Choose the one alternative that best completes the statement or answers the question.
What is the average translational kinetic energy of an ideal gas at 819 K? The Boltzmann constant is $1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K }$

A) $3.77 \times 10 ^ { - 19 } \mathrm {~J}$
B) $1.13 \times 10 ^ { - 17 } \mathrm {~J}$
C) $1.70 \times 10 ^ { - 20 } \mathrm {~J}$
D) $5.65 \times 10 ^ { - 21 } \mathrm {~J}$

Question 70

Choose the one alternative that best completes the statement or answers the question.
A gas-filled vertical cylinder, closed at the bottom end, is fitted at the top with a piston that can move freely. The mass of the piston is 10.0 kg, and the initial height of the piston above the bottom of the cylinder is 25 cm. A mass of 8.0 kg is placed on the piston. What is the resulting height of the piston, assuming that the temperature of the ideal gas is kept constant?

A) 16 cm
B) 12 cm
C) 14 cm
D) 15 cm
E) 13 cm

Question 71

Choose the one alternative that best completes the statement or answers the question.
A $0.40 - \mathrm { m } ^ { 3 }$ gas tank holds 7.0 moles of ideal diatomic nitrogen gas at a temperature of 290 K. The atomic mass of nitrogen is 14.0 g/mol. What is the pressure of the gas? $( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } , 1 \mathrm {~atm} =$ $101 \text { kPa) }$

A) 37 atm
B) 22 atm
C) 42 atm
D) 32 atm
E) 27 atm

Question 72

Choose the one alternative that best completes the statement or answers the question.
At what temperature is the rms speed of hydrogen molecules, $\mathrm { H } _ { 2 }$ which have a molecular weight of 2.02 g/mole, equal to 2.0 km/s? The Boltzmann constant is $1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K } \text { and } N _ { \mathrm { A } } = 6.022 \times$ $10^{23}$ molecules/mol.

A) $17 ^ { \circ } \mathrm { C }$
B) $51 ^ { \circ } \mathrm { C }$
C) $72 ^ { \circ } \mathrm { C }$
D) $34 ^ { \circ } \mathrm { C }$
E) $68 ^ { \circ } \mathrm { C }$

Question 73

Choose the one alternative that best completes the statement or answers the question.
A 3.9-L volume of ideal neon gas (monatomic) is at a pressure of 5.6 aym and a temperature of 330 K. The atomic mass of neon is 20.2 g/mol . The temperature of the gas is now increased to 430 K and the volume is increased to 5.9 L. What is the final pressure of the gas?

A) 6.3 atm
B) 4.3 atm
C) 5.8 atm
D) 5.3 atm
E) 4.8 atm

Question 74

Write the word or phrase that best completes each statement or answers the question.
As shown in the figure, an air pocket at the top of a vertical tube, closed at the upper end and open at the lower, occupies a volume of $560 \mathrm {~cm} ^ { 3 }$ at the surface of a lake where the air pressure is $1.0 \times 10 ^ { 5 } \mathrm {~Pa}$ and the temperature is $37 ^ { \circ } \mathrm { C }$ What is the volume of the air in the pocket if the tube is taken to a depth of 56 meters, where the temperature is $7 ^ { \circ } \mathrm { C } ?$ Assume that none of the air escapes from the tube. The density of the water in the lake is 1000 $\mathrm { kg } / \mathrm { m } ^ { 3 }$

Question 75

Write the word or phrase that best completes each statement or answers the question.
What is the total translational kinetic energy of the gas in a classroom filled with nitrogen at $1.01 \times 10 ^ { 5 } \mathrm {~Pa} \text { at } 20.7 ^ { \circ } \mathrm { C } \text { ? }$ The dimensions of the classroom are $4.60 \mathrm {~m} \times 5.20 \mathrm {~m} \times 8.80 \mathrm {~m}$ The Boltzmann constant is $1.3806503 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K } , R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } , \text { and } N _ { \mathrm { A } } = 6.022 \times$ $10 ^ { 23 }$ molecules/mol.

Question 76

Choose the one alternative that best completes the statement or answers the question.
A $0.50 \mathrm {~m} ^ { 3 }$ gas tank holds 3.0 moles of ideal diatomic nitrogen gas at a temperature of 350 K. The atomic mass of nitrogen is 14.0 g/mol. What is the rms speed of the molecules? (The Boltzmann constant is $\left. 1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K } , N _ { \mathrm { A } } = 6.022 \times 10 ^ { 23 } \mathrm { molecules } / \mathrm { mol } . \right)$

A) 97
B) 21
C) 790
D) 390
E) 560

Question 77

Choose the one alternative that best completes the statement or answers the question.
A sealed container holds 0.020 moles of ideal nitrogen $\left( \mathrm { N } _ { 2 } \right)$ gas, at a pressure of 1.5 atm and a temperature of 290 K. The atomic mass of nitrogen is 14.0 g/mol. How many molecules of nitrogen are in the container? $( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } , 1 \mathrm {~atm} = 101 \mathrm { kPa } )$

A) $6.0 \times 10 ^ { 21 } \mathrm {~mol}$
B) $2.4 \times 10^{22} \mathrm {~mol}$
C) $1.2 \times 10 ^ { 22 } \mathrm {~mol}$
D) $3.0 \times 10 ^ { 21 } \mathrm {~mol}$
E) $1.5 \times 10^{21} \mathrm {~mol}$

Question 78

Choose the one alternative that best completes the statement or answers the question.
A 24.0-L tank contains ideal helium gas at $27 ^ { \circ } \mathrm { C }$ and a pressure of 22.0 atm. How many moles of gas are in the tank? $( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } , 1 \mathrm {~atm} = 101 \mathrm { kPa } )$

A) 138 mol
B) 17.5 mol
C) 21.4 mol
D) 76.0 mol
E) 238 mol

Question 79

Choose the one alternative that best completes the statement or answers the question.
A vertical cylinder, closed at the bottom end, contains 0.0100 mol of ideal gas. It is fitted at the top with a piston that can move freely. The mass of the piston is 14.0 kg and the initial height of the piston above the bottom of the cylinder is 25 cm. What is the temperature of the gas? $( R = 8.31$ $\mathrm { J } / \mathrm { mol } \cdot \mathrm { K } )$

A) 405 K
B) 3620 K
C) 413 K
D) 500 K
E) 290 K

Question 80

Choose the one alternative that best completes the statement or answers the question.
A 5.3 L flask of ideal neon gas (which is monatomic) is at a pressure of 6.0 atm and a temperature of 290 K. The atomic mass of neon is 20.2 g/mol. What is the mass of the neon gas in the flask. $( R =$ $\left. 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } , 1 \mathrm {~atm} = 101 \mathrm { kPa } , N _ { \mathrm { A } } = 6.022 \times 10 ^ { 23 } \mathrm { molecules } / \mathrm { mol } \right)$

A) $1.3 \times 10 ^ { 1 }$
B) $2.7 \times 10 ^ { 1 }$
C) $2.7 \times 10 ^ { 3 }$
D) $1.6 \times 10 ^ { - 2 }$
E) $2.7 \times 10 ^ { - 2 }$