Deck 16: Temperature and the Kinetic Theory of Gases

Question 1

A constant volume gas thermometer has a pressure of 2.00 atm at 100 $\degree$ C.What would its pressure be at 0 $\degree$ C?

A)0.732 atm
B)1.46 atm
C)1.24 atm
D)1.37 atm
E)More information is needed to find the answer.

Answer 1

1.46 atm

Question 2

A beaker is filled to the 500 ml mark with alcohol.What increase in volume (in ml)does the beaker contain when the temperature changes from 5 $\degree$ C to 30 $\degree$ C? (Neglect the expansion of the beaker,evaporation of alcohol and absorption of water vapor by alcohol. ) $\beta$ _alcohol = 1.12 *10^-4/ $\degree$ C

A)0.47
B)0.93
C)1.4
D)1.7
E)2.5

Answer 2

1.4

Question 3

A thermometer registers a change in temperature of 100 $\degree$ F.What change in temperature does this correspond to on the Kelvin Scale?

A)453
B)328
C)180
D)55.6
E)24.5

Answer 3

55.6

Question 4

A bridge is made with segments of concrete 50 m long.If the linear expansion coefficient is 12 *10 ^{- 6} ( $\degree$ C) ^{- 1},how much spacing (in cm)is needed to allow for expansion during an extreme temperature change of 150 $\degree$ F?

A)10
B)2.5
C)7.5
D)5.0
E)9.5

Question 5

A student has written the equation below to convert a temperature in degrees Fahrenheit into Kelvins.What is wrong with this equation? $T _ { K } = \frac { 9 } { 5 } T _ { F } + 32$

A)The factor in front of T_F should be $\frac { 5 } { 9 }$ .
B)The numerical factor $\frac { 5 } { 9 }$ should multiply (T_F - 32).
C)An additional 273.15 Kelvins must be added to the right side of the equation.
D)All the corrections above are required.
E)Only corrections (b)and (c)are required.

Question 6

In order for two objects to have the same temperature,they must

A)be in thermal equilibrium.
B)be in thermal contact with each other.
C)have the same relative "hotness" or "coldness" when touched.
D)have all of the properties listed above.
E)have only properties (b)and (c)above.

Question 7

A pressure of 10.0 mm Hg is measured at the triple-point of water using a constant-volume gas thermometer.What will the pressure be (in mm Hg)at 50.0 $\degree$ C?

A)68.3
B)1.80
C)31.8
D)11.8
E)8.50

Question 8

A pressure of 10.0 mm Hg is measured using a constant-volume gas thermometer at a temperature of 50.0 $\degree$ C.What is the pressure (in mm Hg)at the zero-point temperature?

A)31.8
B)11.8
C)8.45
D)54.6
E)68.3

Question 9

At what temperature is the Celsius scale reading equal to twice the Fahrenheit scale reading?

A)-12.3 $\degree$ F
B)-24.6 $\degree$ F
C)-12.3 $\degree$ C
D)-6.1 $\degree$ C
E)-20 $\degree$ F

Question 10

Two thermometers are calibrated,one in degrees Celsius and the other in degrees Fahrenheit.At what temperature (in kelvins)do their readings measure the same temperature?

A)218.15
B)233.15
C)273.15
D)40.15
E)0

Question 11

In order to understand the concept of temperature it is necessary to understand

A)the zeroth law of thermodynamics.
B)the first law of thermodynamics.
C)the second law of thermodynamics.
D)all of the above.
E)only (b)and (c)above.

Question 12

A gallon container is filled with gasoline.How many gallons are lost if the temperature increases by 25 $\degree$ F? (The volume expansion of gasoline is 9.6 *10 ^{- 4} ( $\degree$ C) ^{- 1}. )(Neglect the change in volume of the container. )

A)2.4 *10 ^{- 2}
B)1.3 * 10 ^{- 2}
C)3.6 *10 ^{- 2}
D)4.8 *10 ^{- 2}
E)9.6 *10 ^{- 2}

Question 13

A temperature difference of 9.0 Celsius degrees is equal to a Fahrenheit temperature difference of

A)5.0 Fahrenheit degrees.
B)9.0 Fahrenheit degrees.
C)16 Fahrenheit degrees.
D)37 Fahrenheit degrees.
E)41 Fahrenheit degrees.

Question 14

Two bodies can be in thermal equilibrium with one another when they are at the same temperature even if they

A)absorb different quantities of thermal energy from their surroundings in equal time intervals.
B)have different masses.
C)have different volumes.
D)have any of the properties listed above.
E)have any of the properties listed above and one of them is contact with a third body at a different temperature.

Question 15

A child has a temperature of 104 $\degree$ F.What is the temperature in degrees kelvin?

A)40
B)406
C)401
D)313
E)349

Question 16

A building made with a steel structure is 650 m high on a winter day when the temperature is 0 $\degree$ F.How much taller (in cm)is the building when it is 100 $\degree$ F? (The linear expansion coefficient of steel is 11 *10 ^{- 6} ( $\degree$ C) ^{- 1}. )

A)71
B)36
C)40
D)46
E)65

Question 17

A bowling ball size probe from a spaceship and a pebble size object land on a large asteroid that is far from any star.After a long period of time has passed,it is highly probable that the pebble and the probe

A)have each had the same change in temperature.
B)have each had the same change in volume.
C)are in thermal equilibrium with one another.
D)are not in thermal equilibrium with one another.
E)are in thermal equilibrium with one another,but are not at the same temperature.

Question 18

Death Valley in California receives many German tourists.When you convert a summer temperature reading of 130 $\degree$ F to the Celsius scale they use at home,you find that the Celsius temperature is about

A)26 $\degree$ 0 C.
B)54 $\degree$ C.
C)72 $\degree$ C.
D)176 $\degree$ C
E)327 $\degree$ C.

Question 19

A temperature difference of 5 K is equal to

A)a difference of 9 on the Celsius scale.
B)a difference of 9 on the Fahrenheit scale.
C)a difference of 2.8 on the Rankine scale.
D)a difference of .5 on the Fahrenheit scale.
E)a difference of 2.8 on the Celsius scale.

Question 20

Helium condenses into the liquid phase at approximately 4 K.What temperature,in degrees Fahrenheit,does this correspond to?

A)-182
B)-269
C)-118
D)-452
E)-484

Question 21

One mole of an ideal gas has a temperature of 25 $\degree$ C.If the volume is held constant and the pressure is doubled,the final temperature (in $\degree$ C)will be

A)174
B)596
C)50
D)323
E)25

Question 22

A bicycle pump contains air at one atmosphere and 0 $\degree$ C.As the tire is pumped up,the volume of air decreases by 50% with each stroke.What is the new pressure of air (in atm)in the chamber after the first stroke,assuming no temperature change?

A)2
B)1
C)0.5
D)0.1
E)3

Question 23

The temperature of a quantity of an ideal gas is

A)one measure of its ability to transfer thermal energy to another body.
B)proportional to the average molecular kinetic energy of the molecules.
C)proportional to the internal energy of the gas.
D)correctly described by all the statements above.
E)correctly described only by (a)and (b)above.

Question 24

A bubble having a diameter of 1.00 cm is released from the bottom of a swimming pool where the depth is 5.00 m.What will the diameter of the bubble be when it reaches the surface? The temperature of the water at the surface is 20.0 $\degree$ C,whereas it is 15.0 $\degree$ C at the bottom.(The density of water is 1.00 *10³ kg/m³. )

A)1.05 cm
B)1.15 cm
C)1.45 cm
D)1.65 cm
E)1.35 cm

Question 25

Two moles of an ideal gas are placed in a container of adjustable volume.When measurements are made

A)the pressure is inversely proportional to the volume at constant temperature.
B)the temperature is directly proportional to the volume at constant pressure.
C)the temperature is directly proportional to the pressure at constant volume.
D)all the statements above are found to be correct.
E)only statements (a)and (b)are found to be correct.

Question 26

A helium-filled balloon has a volume of 1 m³.As it rises in the earth's atmosphere,its volume expands.What will its new volume be (in m³)if its original temperature and pressure are 20 $\degree$ C and 1 atm,and its final temperature and pressure are -40 $\degree$ C and 0.1 atm?

A)4
B)6
C)8
D)10
E)1.5

Question 27

One mole of an ideal gas is held at a constant volume of 1 liter.Find the change in pressure if the temperature increases by 50 $\degree$ C.

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

Question 28

A container having a volume of 1.0 m³ holds 5.0 moles of helium gas at 50 $\degree$ C.If the helium behaves like an ideal gas,the total energy of the system is

A)2.0 * 10⁴ J.
B)2.5 *10⁴ J.
C)1.7 * 10³ J.
D)1.5 * 10³ J.
E)4.0 *10⁴ J.

Question 29

The mass of a sulfur atom is 32.0 u,and the mass of a fluorine atom is 19.0 u.What is the mass of a mole of sulfur hexafluoride (UF₆)?

A)41.0 g
B)20.5 g
C)106 g
D)146 g
E)211 g

Question 30

Two identical containers,A and B,hold equal amounts of the same ideal gas at the same P_o,V_o and T_o.The pressure of A then decreases by a half while its volume doubles;the pressure of B doubles while its volume decreases by a half.Which statement correctly describes the temperatures of the gases after the changes?

A)T_A = 0.5T_B = T_o.
B)T_B = 0.5T_A = T_o.
C)T_B = T_A = T_o.
D)T_A = 2T_B = T_o.
E)T_B = 2T_A = T_o.

Question 31

An auditorium has dimensions 10 m *10 m *60 m.How many moles of air fill this volume at one atmosphere and 0 $\degree$ C?

A)2.7 * 10²
B)2.7 * 10⁴
C)2.7 * 10³
D)2.7 * 10⁵
E)2.7* 10⁶

Question 32

At which of the following temperatures would one liter of water weigh the most?

A)2 $\degree$ C
B)4 $\degree$ C
C)8 $\degree$ C
D)90 $\degree$ C
E)It would weigh the same at all these temperatures.

Question 33

A scuba diver has his lungs filled to half capacity (3 liters)when 10 m below the surface.If the diver holds his breath while quietly rising to the surface,what will the volume of the lungs be (in liters)at the surface? Assume the temperature is the same at all depths.(The density of water is 1.0 *10³ kg/m³. )

A)5.9
B)4.5
C)6.4
D)3.9
E)3.1

Question 34

When the coefficient of linear expansion, $\alpha$ ,and the temperature change,T_f - T_i,are large,a length L_i of a solid substance expands in length to

A)L_f = $\alpha$ L_i(T_f - T_i).
B)L_f = L_i[1 + $\alpha$ (T_f - T_i)].
C)L_f = L_i[1 + ln( $\alpha$ (T_f - T_i))].
D) $L _ { f } = L _ { i } e ^ { \alpha \left( T _ { f } - T _ { 1 } \right) }$ .
E) $L _ { f } = L _ { i } \left[ 1 + e ^ { \alpha \left( T _ { f } - T _ { i } \right) } \right]$ .

Question 35

A container having a volume of 1.0 m³ holds 5.0 moles of helium gas at 50 $\degree$ C.If the helium behaves like an ideal gas,the average kinetic energy per molecule is

A)6.7 *10^-20 J.
B)1.0 *10^-21 J.
C)1.0 * 10^-20 J.
D)6.7 *10^-21 J.
E)1.3 * 10^-20 J.

Question 36

Angela claims that she wears a cylindrical-shaped hollow gold bracelet because it expands less than a solid one with a change in temperature.Clarissa claims that a cylindrical-shaped solid gold bracelet expands less than a hollow one.Which one,if either,is correct?

A)Angela,because the bracelet expands outward on its outer surface and inward on its inner surface.
B)Clarissa,because the bracelet expands outward on its outer surface and inward on its inner surface.
C)Angela,because the inner circumference does not change,but the outer circumference expands.
D)Clarissa,because the inner circumference does not change,but the outer circumference expands.
E)Neither,because both the inner and outer circumferences increase in length.

Question 37

One mole of an ideal gas is held at a constant pressure of 1 atm.Find the change in volume (in liters)if the temperature changes by 50 $\degree$ C.

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

Question 38

A square plate has an area of 29.00 cm² at 20.0 $\degree$ C.It will be used in a low temperature experiment at T = 10.0K where it must have an area of 28.00 cm².What area must be removed form the plate at 20.0 $\degree$ C for it to have the correct area at 10.0 K? (The coefficient of linear expansion is 10 *10 ^{- 6} ( $\degree$ C) ^{- 1}. )

A)0.079 3 cm²
B)0.159 cm²
C)0.238 cm²
D)0.841 cm²
E)0.921 cm²

Question 39

An auditorium has a volume of 6 *10³ m³.How many molecules of air are needed to fill the auditorium at one atmosphere and 0 $\degree$ C?

A)1.6 *10²⁹
B)1.6 * 10²⁷
C)1.6 * 10²⁵
D)1.6 * 10²³
E)1.6 * 10²⁰

Question 40

What is the change in area (in cm²)of a 60.0 cm by 150 cm automobile windshield when the temperature changes from 0 $\degree$ C to 36.0 $\degree$ C.The coefficient of linear expansion of this glass is 9.0 *10 ^{- 6}/ $\degree$ C.

A)1.6
B)2.9
C)3.2
D)4.9
E)5.8

Question 41

The average molecular translational kinetic energy of a molecule in an ideal gas is

A) $\frac { 3 } { 2 }$ k_BT.
B) $\frac { 3 } { 2 }$ RT.
C) $\frac { 5 } { 2 }$ k_BT.
D) $\frac { 5 } { 2 }$ RT.
E) $\frac { n + 3 } { 2 }$ k_BT,where n = number of internal degrees of freedom.

Question 42

Which statement below is NOT an assumption made in the molecular model of an ideal gas?

A)The average separation between molecules is large compared with the dimensions of the molecules.
B)The molecules undergo inelastic collisions with one another.
C)The forces between molecules are short range.
D)The molecules obey Newton's laws of motion.
E)Any molecule can move in any direction with equal probability.

Question 43

When we consider a thin horizontal layer of the atmosphere,of thickness dy,of area A,with pressure P on the bottom,with an average mass m per molecule,and n_V molecules per unit volume,the magnitude of the difference of the pressure at the top and bottom of the layer is given by dP =

A)mgdy.
B)mgn_Vdy.
C)mgAdy.
D)mgn_VAdy.
E)mgn_VAPdy.

Question 44

If the rms speed of helium atoms is v_rms,He at temperature T,what is the rms speed of CO₂ at the same temperature?

A) $$\nu _ { \operatorname { rms} , H e } / 44$$
B) $$\nu _ { \operatorname { rms} , H e } / 11$$
C) $v _ { \operatorname { rms} , H { e } } / \sqrt { 44 }$
D) $v _ { \operatorname { rms} , H { e } } / \sqrt { 11 }$
E) $\nu _ { \operatorname { rms} , \mathrm { He } } / \sqrt { 22 }$

Question 45

According to kinetic theory,a typical gas molecule in thermal equilibrium at room temperature has a kinetic energy K = 6.00 *10 ^{- 21} J,regardless of mass.Estimate the speed at room temperature of a hydrogen molecule H₂ (m = 3.34 *10 ^{- 27} kg)and a xenon atom (m = 2.00 *10 ^{- 25} kg).[k_B = 1.38 *10 ^{- 23} J/K]

Question 46

Suppose the ends of a 30-m long steel beam are rigidly clamped at 0 $\degree$ C to prevent expansion.The beam has a cross-sectional area of 30 cm².What force against the clamps does the beam exert when it is heated to 40 $\degree$ C? ( $\alpha$ _Steel = 1.1 * 10 ^{- 5}/ $\degree$ C,Y_steel = 20 *10¹⁰ N/m²).

Question 47

The average kinetic energy of a nitrogen molecule at room temperature (20 $\degree$ C)is

A)2 *10 ^{- 21} J.
B)4 *10 ^{- 21} J.
C)6 * 10 ^{- 21} J.
D)8 *10 ^{- 21} J.
E)1 *10 ^{- 20} J.

Question 48

During the volcanic eruption of Mt.Pelee in 1902,an incredibly hot "burning cloud" rolled down the mountain and incinerated the town of Saint-Pierre.From the damage done,the temperature in the cloud was estimated at 700 $\degree$ C.If the air temperature was 20 $\degree$ C and a mole of air is 29 grams,estimate the molecular weight of the gas in the "burning cloud" that made it heavier than the surrounding air.(As a follow-on,estimate the most probable composition of the cloud.Some typical volcanic gases are H₂S,SO₂,H₂SO₄,CO₂,NO. )

Question 49

A 50-gram sample of dry ice (solid CO₂)is placed in a 4-liter container.The system is sealed and allowed to reach room temperature (20 $\degree$ C).By approximately how much does the pressure inside the container increase when the dry ice turns to gas? (Ignore the initial volume of the sample. )

Question 50

A gold ring has an inner diameter of 2.168 cm at a temperature of 15.0 $\degree$ C.Determine its diameter at 100.0 $\degree$ C.( $\alpha$ _GOLD = 1.42 * 10 ^{- 5}/ $\degree$ C)

Question 51

Determine the change in length of a 20-m railroad track made of steel if the temperature is changed from -15 $\degree$ C to +35 $\degree$ C.( $\alpha$ _STEEL = 1.1 *10 ^{- 5}/ $\degree$ C)

Question 52

The pressure of a substance is directly proportional to its volume when the temperature is held constant and inversely proportional to its temperature when the volume is held constant.Is this substance an ideal gas? Explain why your answer is correct.

Question 53

The root mean square speed of a gas molecule is greater than the average speed,because the former gives a greater weight to

A)lighter molecules.
B)heavier molecules.
C)lower speeds.
D)higher speeds.
E)more probable speeds.

Question 54

At what Fahrenheit temperature are the Kelvin and Fahrenheit temperatures numerically equal?