Deck 17: Temperature, Thermal Expansion, and the Ideal Gas Law

Question 1

At constant volume, the absolute pressure of a gas is inversely proportional to the absolute temperature.

Answer 1

False

Question 2

When a bimetallic strip is cooled, the strip will bend toward the side

A)with the larger coefficient of linear expansion.
B)with the smaller coefficient of linear expansion.
C)with the higher temperature.
D)with the lower temperature.
E)depends of the method of heating

Answer 2

with the larger coefficient of linear expansion.

Question 3

Two systems are in thermal equilibrium. The two systems are at the same

A)pressure.
B)volume.
C)height.
D)pressure and temperature.
E)temperature.

Answer 3

temperature.

Question 4

Equal volumes of gas at the same pressure and temperature contain equal numbers of molecules.

Question 5

Distinguish between the three phases of matter from the atomic or microscopic point of view.

Question 6

Describe the anomalous thermal expansion property of water and its significance.

Question 7

State Charles's law.

Question 8

State Gay-Lassac's law.

Question 9

State Avogadro's hypothesis.

Question 10

State Boyle's law.

Question 11

When a bimetallic strip is heated, the strip will bend toward the side

A)with the larger coefficient of linear expansion.
B)with the smaller coefficient of linear expansion.
C)with the higher temperature.
D)with the lower temperature.
E)depends of the method of heating

Question 12

A machinist needs to remove a tight fitting pin of material A from a hole in a block made of material B. The machinist heats both the pin and and the block to the same high temperature and removes the pin easily. What statement relates the coefficient of thermal expansion of material A to that of material B?

A)Material B has a greater coefficient of expansion than does material A.
B)The situation is not possible, heating block B will shrink the hole in the material as the material expands with increasing temperature.
C)Material B has the same coefficient of expansion as does material A.
D)Material B has a negative coefficient of expansion and A has a positive coefficient of expansion.
E)Material A has a greater coefficient of expansion than does material B.

Question 13

State the Zeroth Law of Thermodynamics.

Question 14

The volume of a given amount of gas is inversely proportional to the absolute temperature when the pressure is kept constant.

Question 15

If a thermometer measures the temperature of two objects as being equal, you can conclude that the objects will be in thermal equilibrium if they are brought into thermal contact.

Question 16

The triple point of water occurs only at a unique temperature and pressure.

Question 17

Describe the two step process used to calculate thermal stress in a beam with ends which are rigidly fixed.

Question 18

If a thermometer measures the temperature of two objects as being equal, you can conclude that if the objects are placed in thermal contact, no heat will flow between them.

Question 19

The volume of a gas is inversely proportional to the absolute pressure applied to it when the temperature is kept constant.

Question 20

Explain the operation of a constant-volume gas thermometer.

Question 21

What is wrong with the following statements? A fixed quantity of ideal gas at constant volume is warmed from a temperature of 20°C to 40°C. The pressure in the gas doubles during this process because the temperature doubles.

A)The appropriate temperature does not double during this process, so the pressure does not double either.
B)It is impossible to keep a fixed quantity of gas at constant volume during the temperature change specified in the problem.
C)The pressure changes to one half its initial value during this process.
D)The conclusion regarding the pressure cannot be reached because the mass of the ideal gas particles is unknown.
E)The pressure change will depend on whether the ideal gas particles are monatomic or polyatomic.

Question 22

FIGURE 17-1
Consider a flat steel plate with a hole through its center as shown in Fig.17-1. 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 if it takes up less than half the plate's surface area.
C)contract.
D)expand.
E)remain the same size.

Question 23

Express 14°F in °C.

A)-18°C
B)-10°C
C)46°C
D)14°C
E)57°C

Question 24

An industrial fabrication process stamps out thin metal pieces, each in the shape of a square with a circular hole in the middle, from a large thin sheet. These pieces are mounted in a large machine. As these pieces heat up during regular machine operation, the diameter of the circular hole will

A)decrease.
B)stay the same.
C)increase.
D)behave unpredictably causing the machine to malfunction.

Question 25

FIGURE 17-1
Consider a flat steel plate with a hole through its center as shown in Fig. 17-1. When the plate's temperature is increased, the hole will

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

Question 26

Two liters of a perfect gas are at 0°C and 1 atm. The gas is nitrogen, N_2.
(a) Determine the number of moles.
(b) Determine the number of molecules.
(c) Determine the mass of the gas.

Question 27

A metal cylindrical sleeve has an inner radius A and an outer radius B. The metal has a positive thermal expansion coefficient. When the sleeve's temperature increases

A)the outer radius decreases and the inner radius increases.
B)the inner radius decreases and the outer radius increases.
C)both the inner and outer radii decrease.
D)both the inner and outer radii increase.
E)The sleeve's length decreases.

Question 28

Gallium boils at 2205°C. What is the corresponding temperature in the Fahrenheit scale?

A)2205°F
B)3805°F
C)4001°F
D)5223°F
E)5548°F

Question 29

On a cold winter day, you turn up the thermostat in your house. Assume that your house is well sealed and that no air enters or leaves the house. When the air temperature in your house rises a short while later, what statement is correct regarding the air pressure?

A)The air pressure is higher at the higher temperature.
B)The air pressure is lower at the higher temperature.
C)The air pressure does not change at the higher temperature.
D)The air pressure increases at first but then decreases again as the temperature approaches its higher value.
E)The air pressure decreases at first but then increases again as the temperature approaches its lower value.

Question 30

Two metal spheres are made of the same material and have the same diameter, but one is solid and the other is hollow. If their temperature is increased by the same amount,

A)the solid sphere becomes bigger than the hollow one.
B)the hollow sphere becomes bigger than the solid one.
C)the two spheres remain of equal size.
D)the solid sphere becomes heavier and the hollow one lighter.
E)the solid sphere becomes lighter and the hollow one heavier.

Question 31

The number of molecules in one mole of a substance

A)depends on the molecular weight of the substance.
B)depends on the atomic weight of the substance.
C)depends on the density of the substance.
D)depends on the temperature of the substance.
E)is the same for all substances.

Question 32

Express 50°C in °F.

A)50°F
B)45.6°F
C)59.8°F
D)122°F
E)148°F

Question 33

Nitrogen boils at -196°C. What is the corresponding temperature in the Fahrenheit scale?

A)-315°F
B)-196°F
C)-346°F
D)-290°F
E)-321°F

Question 34

Internal human body temperature is often stated to be normal at 98.6°F. What is this temperature on the Celsius scale?

A)120°C
B)145°C
C)37.0°C
D)72.6°C
E)22.8°C

Question 35

When both the pressure and the absolute temperature of an ideal gas are increased each by a factor of two, the volume occupied by the gas will

A)increase by a factor of four.
B)increase by a factor of two.
C)not change.
D)decrease by a factor of two.
E)decrease by a factor of four.

Question 36

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

A)a temperature warmer than 3°C
B)a temperature less than 3°C
C)a temperature equal to 3°C
D)There is not enough information to determine.

Question 37

For a fixed amount of gas, if the absolute temperature of the gas is doubled, what happens to the pressure of the gas?

A)The answer cannot be determined without volume information.
B)The pressure of the gas becomes double the original pressure.
C)The pressure of the gas becomes triple the original pressure.
D)The pressure of the gas becomes one half the original pressure.
E)The pressure of the gas becomes four times the original pressure.

Question 38

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

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

Question 39

On a hot summer day, you turn the thermostat in your house way down. Assume that your house is well sealed and that no air enters or leaves the house. When the air temperature in your house falls a short while later, what statement is correct regarding the air pressure?

A)The air pressure is higher at the lower temperature.
B)The air pressure is lower at the lower temperature.
C)The air pressure does not change at the lower temperature.
D)The air pressure increases at first but then decreases again as the temperature approaches its higher value.
E)The air pressure decreases at first but then increases again as the temperature approaches its lower value.

Question 40

A mole of diatomic oxygen molecules and a mole of diatomic nitrogen molecules at STP have

A)the same average molecular speeds.
B)the same number of molecules.
C)the same diffusion rates.
D)all of the above
E)none of the above

Question 41

The coefficient of volume expansion of olive oil is 0.68 × 10^-3K^-1. A 1-liter 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 C°. As a result, 0.0167 liters of olive oil spill over the top of the beaker. What is the coefficient of linear expansion of glass?

A)1 × 10^-6K^-1
B)4 × 10^-6K^-1
C)1 × 10^-5K^-1
D)2 × 10^-5K^-1
E)3 ×10^-5K^-1

Question 42

A rod has a length 2.0000 m at 20.0°C. The length of the rod increases to 2.0005 m when the temperature increases to 40.0°C. What is the coefficient of thermal expansion of the material from which the rod is made?

A)2.00 × 10^-5/K
B)2.50 × 10^-5/K
C)1.25 × 10^-5/K
D)5.00 × 10^-3/K
E)5.00 × 10^-5/K

Question 43

The coefficient of linear expansion of steel is 12 × 10^-6K^-1. What is the change in length of a 25-m steel bridge span when it undergoes a temperature change of 40 K?

A)1.2 cm
B)1.4 cm
C)1.6 cm
D)1.8 cm
E)2.0 cm

Question 44

The density of water at 0°C is 999.84 kg/m³ and at 4°C it is 999.96 kg/m³. A 1.0-liter container, full to the brim with water at 4°C is placed in the refrigerator. By the time that the temperature of the water reaches 0°C, how much of the water has spilled from the container, assuming that the contraction of the container is negligible?

A)1.1 × 10^-7m³
B)1.2 × 10^-7m³
C)1.3 × 10^-7m³
D)1.4 × 10^-7m³
E)1.5 × 10^-7m³

Question 45

The coefficient of linear expansion of lead is 29 × 10^-6K^-1. What change in temperature will cause a 10-m long lead bar to change in length by 3.0 mm?

A)5.0 K
B)10 K
C)15 K
D)20 K
E)25 K

Question 46

Suppose that a steel bridge, 1000 m long, were built without any expansion joints. Suppose that only one end of the bridge was held fixed. What would the difference in the length of the bridge be between winter and summer, taking a typical winter temperature as 0°C, and a typical summer temperature as 40°C? The coefficient of thermal expansion of steel is 10.5 × 10^-6K^-1.

A)0.42 m
B)0.11 mm
C)0.11 m
D)0.42 mm
E)0.37 cm

Question 47

1 L of water at 20°C will occupy what volume at 80°C? Water has a volume expansion coefficient of 210 × 10^-6/C°.

A)1.6 L
B)1.326 L
C)1.013 L
D)0.987 L
E)0.9987 L

Question 48

FIGURE 17-2
A bolt hole in a brass plate has a diameter of 1.200 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 /C°.)

A)1.205 cm
B)1.125 cm
C)1.195 cm
D)1.200 cm
E)1.210 cm

Question 49

FIGURE 17-2
Two identical concrete slabs lie flat and in contact with each other as shown in Fig. 17-2. If the temperature increases by 40°C, the lower edges opposite the contact edges remained fixed in position, and the lower edges of the contact side remain in contact, at what angle φ will the slabs be tilted? The coefficient of thermal expansion of the concrete is 10 × 10^-6/K.

A)18.7°
B)0.0283°
C)14.5°
D)1.62°
E)answer depends on length of slabs

Question 50

A bimetallic strip is made out of two strips of metal bonded together. Each strip is 20.0 cm long and 1.00 mm thick. One strip has a coefficient of thermal expansion 4.00 × 10^-6/K and the other has a coefficient of thermal expansion 3.00 × 10^-6/K. At 20.0°C the strip is straight. What is the inner radius of curvature of the composite strip at 200°C?

A)15.2 cm
B)2.22 m
C)1.27 m
D)34.8 cm
E)5.56 m

Question 51

A bimetallic strip is made by bonding together a 1.0-mm thick and 15.0-cm long steel strip to a similar strip made of aluminum. The strip is straight when the temperature is 20.0°C. What will the radius of curvature of the strip be when the temperature is 40.0°C? The coefficient of thermal expansion of steel is 10.5 × 10^-6K^-1 and that of aluminum is 23.0 × 10^-6K^-1.

A)4.0 m
B)3.6 m
C)4.8 m
D)5.2 m
E)4.4 m

Question 52

You want to insert an aluminum rod, which at 20°C has a radius of 1.00020 cm into a copper tube which has a radius of 1.00010 cm at the same temperature. You decide to put both of them in the refrigerator. At what temperature will the rod just fit if both are cooled to the same temperature? The coefficient of thermal expansion for aluminum is 2.4 × 10^-5K^-1, and that of copper is 1.7 × 10^-5K^-1.

A)7.8°C
B)6.3°C
C)9.2°C
D)14.7°C
E)5.7°C

Question 53

The temperature changes from 35°F during the night to 75°F during the day. What is the temperature change on the Celsius scale?

A)72 C°
B)40 C°
C)32 C°
D)22 C°

Question 54

Water at room temperature of 20.0°C is poured into an aluminum cylinder which has graduation markings etched on the inside. The reading in the graduations is 300.0 cc. The cylinder with the water in it is then immersed in a constant temperature bath at a temperature of 100°C. What is the reading for the level of water on the graduations of the cylinder after the water and the cylinder reach thermal equilibrium with the bath? The volume coefficient of expansion of water is 2.07 × 10^-4K^-1, and the linear coefficient of expansion of aluminum is 23.0 × 10^-6K^-1.

A)305.0 cc
B)303.5 cc
C)304.0 cc
D)304.5 cc
E)303.3 cc

Question 55

A thermometer is made such that the freezing point of water is defined to be 60.0°H and the boiling point of water at sea level is defined to be 520°H. What is the Celsius temperature at 240°H?

A)-13.8°C
B)34.6°C
C)31.0°C
D)-7.8°C
E)39.1°C

Question 56

A student finds a blank liquid bulb thermometer and calibrates the scale by placing it in ice water and placing a reference mark at the level of the fluid. The student places the thermometer in boiling water and finds that the fluid level is 12.0 cm above the reference mark. What is the temperature when the fluid level is 2.4 cm above the reference mark?

A)2.4°C
B)24°C
C)25°C
D)28°C
E)20°C

Question 57

The Concorde's exterior is made of aluminum, which has a coefficient of linear expansion of 24 × 10^-6K^-1. At 15°C, the Concorde measures 62.1 m in length. When the plane is in flight, friction with the air increases the temperature of the exterior skin to 200°C. What is the change in the length of the outer skin of the Concorde?

A)20 cm
B)24 cm
C)28 cm
D)32 cm
E)36 cm

Question 58

The volume measuring system for a gasoline pump at the service station is calibrated at 20.0°C. If the temperature of the gasoline drops to 10.0°C, what percentage extra amount of mass of gasoline do you receive when making a purchase? The coefficient of volume expansion for gasoline is 9.5 × 10^-4/K.

A)1.33%
B)1.90%
C)1.05%
D)2.24%
E)0.95%

Question 59

The coefficient of linear expansion of aluminum is 24 × 10^-6K^-1 and the coefficient of volume expansion of olive oil is 0.68 × 10^-3K^-1. A novice cook, in preparation for deep-frying some potatoes fills a 1.00-liter aluminum pot to the brim and heats the oil and the pot from an initial temperature of 15°C to 190°C. To his consternation some olive oil spills over the top. How much?

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

Question 60

400 cm³ of mercury at 0°C will expand to what volume at 50°C? Mercury has a volume expansion coefficient of 180 × 10^-6/C°.

A)450 cm³
B)422.8 cm³
C)409.7 cm³
D)403.6 cm³
E)401.8 cm³

Question 61

A car starts out when the air temperature is 288 K. The air pressure in the tires is 460 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 the volume remains constant?

A)476 kPa
B)563 kPa
C)488 kPa
D)498 kPa
E)512 kPa

Question 62

Internal human body temperature is often stated to be normal at 98.6°F. What is this temperature on the Kelvin scale?

A)346 K
B)393 K
C)310 K
D)296 K
E)418 K

Question 63

On a cold day, when the air temperature is 0°C, you empty your lungs and take a deep breath, filling your lungs with 4.2 L of air. If you hold your breath until the temperature of the air in your lungs reaches 37°C, what is the volume of the air in your lungs at that point, assuming the pressure does not change?

A)4.6 L
B)4.4 L
C)5.0 L
D)4.8 L
E)5.2 L

Question 64

Convert 14°C to K.

A)46 K
B)100 K
C)187 K
D)287 K
E)474 K

Question 65

An ideal gas occupies 400 L at an absolute pressure of 500 kPa. Find the absolute pressure if the volume changes to 950 L and the temperature remains constant.

A)500 kPa
B)210 kPa
C)760 kPa
D)950 kPa
E)1150 kPa

Question 66

An ideal gas in a container of volume 100 cm³ at 20°C has a pressure of 100 N/m². Determine the number of gas molecules in the container.

A)2.4 × 10⁶
B)4.2 × 10⁶
C)6.0 × 10²³
D)2.5 × 10¹⁸
E)5.2 × 10¹⁸

Question 67

A sample of helium (He) occupies 44.8 L at STP. What is the mass of the sample?

A)2 g
B)4 g
C)6 g
D)8 g
E)10 g

Question 68

An ideal gas is at a pressure 1.00 × 10⁵ N/m² and a volume 2.00 m³. If the gas is compressed to a volume 1.00 m³ while the temperature remains constant, what will be the new pressure in the gas?

A)0.500 × 10⁵ N/m²
B)4.00 × 10⁵ N/m²
C)1.00 × 10⁵ N/m²
D)2.00 × 10⁵ N/m²
E)The answer depends on the mass of the gas particles.

Question 69

Convert 14°F to K.

A)263 K
B)287 K
C)163 K
D)-10 K
E)474 K

Question 70

Carbon dioxide solidifies at 195 K. Express this temperature in degrees Fahrenheit.

A)-78°F
B)-40°F
C)-109°F
D)-163°F
E)-351°F

Question 71

A constant volume closed container of gas is at a pressure 1.00 × 10⁵ N/m² and a temperature 20°C. What is the pressure if the temperature of the gas is increased to 60.0°C?

A)0.330 × 10⁵ N/m²
B)9.00 × 10⁵ N/m²
C)0.880 × 10⁵ N/m²
D)3.00 × 10⁵ N/m²
E)1.14 × 10⁵ N/m²

Question 72

What is the temperature of 3.00 moles of an ideal gas at a pressure of 250 kPa held in a volume of 25.0 L?

A)509 K
B)90.5 K
C)752 K
D)272 K
E)251 K

Question 73

How many moles of H₂O molecules are in a 4.00 m³ container at a pressure 8.00 × 10⁵ N/m² and temperature 600°C?

A)7.72 × 10²⁶
B)641
C)441
D)3.86 × 10²⁶
E)2.65 × 10²⁶

Question 74

Convert 14 K to °C.

A)46°C
B)287°C
C)25°C
D)-225°C
E)-259°C

Question 75

What is the mass density of argon gas at pressure 1.00 × 10⁵ N/m² and at temperature 300 K? The mean atomic mass of argon is 39.948u.

A)1.40 kg/m³
B)1.00 kg/m³
C)1.20 kg/m³
D)1.60 kg/m³
E)1.80 kg/m³

Question 76

The interior of a refrigerator has a volume of 0.600 m³. The temperature inside the refrigerator in 282 K, and the pressure is 101 kPa. If the molecular weight of air is 29 g/mol, what is the mass of air inside the refrigerator?

A)498 g
B)560 g
C)135 g
D)267 g
E)750 g

Question 77

A thermometer is made such that the freezing point of water is defined to be 60.0°H and the boiling point of water at sea level is defined to be 520°H. What is absolute zero on the H scale?

A)0.6°H
B)-36°H
C)-980°H
D)-1256°H
E)-1196°H

Question 78

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

A)36N_A
B)2N_A
C)6N_A
D)18N_A
E)none of the above

Question 79

A weather balloon contains 12.0 m³ of hydrogen gas when it is released from a location at which the temperature is 22°C and the pressure is 101 kPa. It rises to a location where the temperature is -30°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)14.0 m³
B)2.38 m³
C)49.9 m³
D)82.6 m³
E)4.16 m³

Question 80

Convert 14 K to °F.

A)287°F
B)-434°F
C)-343°F
D)-259°F
E)474°F