Temperature and the Kinetic Theory of Gases

Transcription

1 Temperature and the Kinetic Theory of Gases 1. What is the force, in N, exerted on a 1 m 2 area by the atmosphere when the atmospheric pressure is 10 5 Pa? a b c d e 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 specific heat. d. have the same relative hotness or coolness when touched. e. have properties (a), (b) and (c) above. 3. When a steel tape measure calibrated at 22 C is used at 28 C, the magnitudes of length measurements made at 28 C, compared to readings made with a tape measure calibrated at 28 C, will be a. too large. b. too small. c. the same at 28 C as at 22 C. d. meaningful only if further information is available to interpret the results. e. unusable because the tape will have been ruined. 4. A balloon remains flexible down to 100 K. What happens to the volume of air inside the balloon when its temperature is changed from 100 K to 200 K? a. It increases. b. It decreases. c. It liquifies. d. It changes state. e. It remains unchanged. 295

2 296 Temperature and the Kinetic Theory of Gases 5. One atmosphere is the same as Pa. What force in N does the atmosphere exert on the top of a sealed can of radius m? a b c d e The pressure in a constant volume thermometer is Pa at 400 K and Pa at 300 K. What is the temperature in K when the pressure is Pa? a. 150 b. 200 c. 250 d. 325 e What K temperature is equivalent to 100 C? a b c d e The temperature of a beaker of water drops from 100 C to 95 C. What is the magnitude of the change in temperature in K? a. 9 b. 5 c. 4 d. 1.8 e The temperature in C equivalent to 98.6 F is a b c d e. 42.0

3 Chapter The temperature in C equivalent to 40 F is a. 30 b. 35 c. 40 d. 45 e What change in F corresponds to a 5 C temperature change? a. 4 b. 5 c. 7 d. 8 e. 9 ANS: e 12. What K temperature is 50 F? a. 273 b c. 228 d e A certain mixture boils at K. At what temperature in C does it boil? a. 10 b. 15 c. 20 d. 25 e A certain mixture boils at K. At what temperature in F does it boil? a. 68 b. 20 c. 42 d. 25 e. 36

4 298 Temperature and the Kinetic Theory of Gases 15. A steel tape is calibrated at 22 C. It is used to measure a 10 m distance when the temperature is 10 C. By what amount in m is the measurement incorrect if the coefficient of linear expansion is a Cf 1? a b c d e a f? 16. A steel column is m high at 0 C. How high is it at 50 C if α = C 1 a b c d e a f. If a 50 liter tank is filled when the 17. The coefficient of volume expansion of gasoline is C 1 temperature is 10 C, how much gasoline in liters will spill when the temperature rises to 31 C? a b c d. 1.0 e A brass ring of coefficient of linear expansion C C. What is its change in diameter in m? a b c d e a f and radius 0.10 m is heated from 10 C to

5 Chapter A round hole of diameter 0.20 m is cut in a piece of brass at 20 C. What would be the change in area in m 2 of the hole if the temperature of the brass were increased to 190 C? The coefficient of linear expansion of brass is a Cf 1? a b c d e The concrete sections of a highway are designed to be 30 m long at 10 C. Expansion slots have to be cut between sections to prevent buckling in the summer when the temperature of the roadway could rise to 60 C. What is the minimum slot width in m that has to be cut if the coefficient of linear expansion is a Cf 1? a b c d e A glass rod is 0.50 m long and m in diameter. The coefficient of linear expansion of the rod is a Cf 1. When the temperature increases by 60 C, its change of length in m is a b c d e A glass rod is 0.50 m long and m in diameter. The coefficient of linear expansion of the rod is a Cf 1. When the temperature increases by 60 C, the change in its diameter in m is a b c d e

6 300 Temperature and the Kinetic Theory of Gases L of gas are at a temperature of 300 K and a pressure of 8 atm. If R = L atm mol K, how many moles of the gas are present? a. 2.5 b. 3.5 c. 4.5 d. 5.5 e. 6.5 ANS: e L of gas are at a temperature of 300 K and a pressure of 8 atm. If R = L atm mol K, how many molecules of the gas are present? a b c d e A kg lump of solid CO 2 is sealed in a 5.0 L evacuated container. The solid CO 2 is heated to 300 K. What is the pressure in atm in the container due to the CO 2 gas if R = L atm mol K? (One mole of CO 2 has a mass of 44 gm.) a. 3.8 b. 4.2 c. 5.6 d. 5.8 e A balloon filled with hydrogen has a volume of 2. 0 m 3 when its temperature is 300 K and its pressure is 1.0 atm. What volume in m 3 would it have at a pressure of 0.11 atm and a temperature of 250 K if R = L atm mol K? a. 10 b. 12 c. 13 d. 14 e. 15 ANS: e

7 Chapter How many molecules of nitrogen would fill a room of dimensions 3. 0 m 10 m 5 m? Its molar mass is 28 g/mol, the temperature is 300 K, R = L atm mol K and the pressure is 1.0 atm. a b c d e An ideal gas with molar mass of 5.0 g/mol has a pressure of 1.5 atm and a volume of 7.9 L at a temperature of 350 K. What is the mass of the gas in kg if R = L atm mol K? a b c d e Five g of water are vaporized in a 2.0 L pressure cooker and heated to 500 K. R = L atm mol K and the molar mass of water is 18 g/mol. What is the pressure in atm inside the container? a. 2.3 b. 3.2 c. 4.5 d. 5.7 e A balloon has a volume of m 3 below the surface of the ocean where the pressure is 5.0 atm. If the temperature remains constant and R = L atm mol K, what is its volume in m 3 when it is at the surface where the pressure is 1.0 atm? a b c d e A balloon has a volume of 2500 L when the temperature is 200 K and the pressure is 0.40 atm. What is its volume in m 3 when the temperature is 300 K and the pressure is 1.0 atm? (R = L atm mol K) a. 2.4 b. 3.8 c. 1.5 d. 2.1 e. 1.7

8 302 Temperature and the Kinetic Theory of Gases 32. A cube with sides of length 0.20 m contains molecules. The temperature is 300 K and k B = J K. What is the force in N on one wall of the cube? a b c d e ANS: e 33. An H 2 molecule at 293 K has a molar mass of speed in m/s? a. 500 b c d. 700 e kg mol. If R = 831. J mol K, what is its rms 34. An N 2 molecule at 300 K has a molar mass of in m/s? a. 517 b c d. 843 e. 771 kg mol. If R = 831. J mol K, what is its rms speed 35. An SO 2 molecule at 293 K has a molar mass of in m/s? a. 270 b. 380 c. 490 d. 390 e. 280 kg mol. If R = 831. J mol K, what is its rms speed 36. At what temperature is the Celsius scale reading equal to twice the Fahrenheit scale reading? a F b F c C d. 6.1 C e. 20 F

9 Chapter A thermometer is made by attaching a capillary tube (diameter mm) to a cm 3 reservoir of mercury. What length in cm is needed for expansion for a change in temperature of 100 C? The volume expansion coefficient of mercury is a Cf 1. (Neglect the expansion of the glass.) a b. 232 c. 174 d. 348 e A building made with a steel structure is 650 m high on a winter day when the temperature is 0 F. How much taller in cm is the building when the temperature is 100 F? (The linear expansion coefficient of steel is a Cf 1.) a. 71 b. 36 c. 40 d. 46 e A clock has a one meter bronze pendulum that is accurate at a temperature of 20 C. What is the change in the length of the pendulum in mm when the temperature reaches 38 C? (The linear expansion coefficient of bronze is a Cf 1.) a b c d e An automobile windshield has dimensions of 60 cm by 150 cm. What minimum tolerance in mm is needed to prevent the windshield from breaking if the temperature changes by 200 F? (The linear expansion coefficient of glass is a Cf 1.) a. 2.0 b. 1.0 c. 1.5 d. 2.5 e. 3.0

10 304 Temperature and the Kinetic Theory of Gases 41. A gallon container is filled with gasoline. How many gallons are lost if the temperature increases by 25 F? (The volume expansion coefficient of gasoline is a Cf 1.) [Neglect the change in volume of the container.] a b c d e An auditorium has dimensions 10 m 10 m 60 m. How many moles of air occupy the auditorium at STP? (R = L atm mol K) a b c d e An auditorium has a volume of m 3. How many molecules of air are needed to fill the auditorium at STP? (R = L atm mol K) a b c d e 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 C? a b. 1.8 c d e A pressure of 10.0 mm Hg is measured using a constant-volume gas thermometer at a temperature of 50.0 C. What is the pressure in mm Hg at the zero-point temperature? a b c d e. 68.3

11 Chapter 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 0.5 on the Fahrenheit scale. e. a difference of 2.8 on the Celsius scale. 47. A thermometer registers a change in temperature of 100 F. What change in temperature does this correspond to on the Kelvin Scale? a. 453 b. 328 c. 180 d. 56 e Helium condenses into the liquid phase at approximately 4 K. What temperature, in degrees Fahrenheit, does this correspond to? a b c d e The boiling point of water is 212 F. Express this in kelvins. a. 100 b. 485 c. 373 d. 173 e 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 b. 233 c. 273 d. 40 e. 0

12 306 Temperature and the Kinetic Theory of Gases 51. The single temperature and pressure at which water, ice, and water vapor can co-exist in equilibrium is called the a. freezing point. b. coequal point. c. boiling point. d. triple point. e. absolute point. 52. A constant volume thermometer can be used to predict the pressure will be zero when the temperature is a. 0 Celsius. b. 0 Fahrenheit. c. 273 Rankine. d. 0 Centigrade. e. 0 Kelvins. ANS: e 53. The scale referred to as absolute temperature is the a. Kelvin scale. b. Centrigrade scale. c. Fahrenheit scale. d. Celsius scale. e. Joule scale. 54. A temperature difference of 5 on the Celsius scale is the same as what temperature difference on the Kelvin scale? a. 3 K b. 5 K c. 9 K d. 12 K e. 18 K 55. A temperature difference of 5 on the Celsius scale is the same as what temperature difference on the Fahrenheit scale? a. 3 F b. 5 F c. 9 F d. 12 F e. 18 F

13 Chapter The volume expansion coefficient of water is negative between 0 C and 4 C. As the temperature of a liter of water increases from 2 C to 3 C, a. the density of the water decreases. b. the volume of the water decreases. c. the volume of the water increases. d. the volume of the water remains constant. e. the density of the water remains constant. 57. An ideal gas is a collection of atoms or molecules a. that move randomly. b. that exert no long-range forces on one another. c. that occupy a negligible fraction of the volume of their container. d. defined by (a), (b) and (c) above taken together. e. defined by (a) and (b) above, but not (c). 58. An isolated container holds 4 moles of hydrogen (m mol = 2 g ) and 2 moles of helium (m mol = 4 g ) at 400 K. The ratio of the total kinetic energy of the hydrogen molecules to the total kinetic energy of the helium molecules is a. 4:1. b. 2:1. c. 1:1. d. 1:2. e. 1: An isolated container holds 2 moles of hydrogen (m mol = 2 g ) and 2 moles of helium (m mol = 4 g ), both as gases in equilibrium. The total kinetic energy is divided equally between the hydrogen molecules and the helium atoms. The ratio of the temperature of the hydrogen molecules to the temperature of the helium atoms is a. 4:1. b. 2:1. c. 1:1. d. 1:2. e. 1:4.

14 308 Temperature and the Kinetic Theory of Gases 60. Steel blocks A and B, which have equal masses, are at T A = 300 C and T B = 400 C. Block C, with mc = 2 ma, is at T C = 350 C. Blocks A and B are placed in contact, isolated and allowed to come to equilibrium. Then they are placed in contact with block C. At that instant, a. TA = TB < TC. b. TA = TB = TC. c. TA = TB > TC. d. TA + TB = TC. e. TA TB = TC. 61. When comparing the root-mean-square speed, v rms, the average speed, v, and the most probable speed, v mp, of molecules in a gas at temperature T, we find that a. vrms < v. b. vrms = v. c. vrms > v. d. vmp > v. e. vmp > vrms. 62. The inner diameter, d R, of a thin aluminum ring equals the diameter, d H, of the hole in an aluminum plate when both are at temperature T. When the temperature of both the plate and ring changes by T, a. dr > dh. b. dr = dh. c. dr < dh. d. d R increases, but d H decreases. e. d R increases, but d H remains constant. 63. A 10 cm bimetallic strip made of aluminum and copper is shown below. The copper, which has a linear expansion coefficient α Cu = a 6 Cf 1, lies above the aluminum, which has α Al = a 6 Cf 1. The strip stays flat at 20 C. When heated to 220 C, the strip Copper Aluminum a. remains flat, but becomes m longer. b. remains flat, but becomes m longer. c. remains flat, but becomes m longer. d. forms an arc with the ends curling upward. e. forms an arc with the ends curling downwards.

15 Chapter A husband and wife team plan to take an old open-cockpit plane up to a 2.0 km height. The lapse rate is 67. C km. What minimum ground temperature must prevail if they are not to reach a temperature below 0 C at the greatest height? a. 0 C b. 6.7 C c C d. 6.7 C e C 65. The meaning of the Maxwell-Boltzmann distribution function, N v, for N molecules in thermal equilibrium follows from the definition of the number of molecules with speeds between v and v+ dv as a. Ndv. b. Nv dv. c. N v N dv. d. N N dv. v e. Nv Ndv. 66. The meaning of the Maxwell-Boltzmann distribution function, N v, for N molecules in thermal equilibrium follows from the definition of the fraction of molecules with speeds between v and v+ dv as a. Ndv. b. Nv dv. c. N v N dv. d. N N dv. v e. dv. N v 67. The left-over radiation from the radiation-dominated era at the start of the universe has a temperature of 2.9 K. In C, this is a b c d e

16 310 Temperature and the Kinetic Theory of Gases 68. The left-over radiation from the radiation-dominated era at the start of the universe has a temperature of 2.9 K. In F, this is a b c d e The temperature at which water freezes and boils may change if there is a change in a. air pressure. b. room temperature. c. quantity of water being frozen or boiled. d. both (a) and (b). e. (a), (b) and (c). 70. Astronauts land on a previously unknown planet and find that its surface is a pure metal. When they take a m long sample at the planetary temperature of C and heat it to C, they find that it changes length by mm. They conclude that the planet is made of a. aluminum (α = a 6 Cf 1 ). b. copper (α = a 6 Cf 1 ). c. gold (α = a 6 1 ). d. lead (α = a 6 Cf 1 ). e. silver (α = C 1 a f ). 71. A container holds a mixture of oxygen (M = 32 g mole) and nitrogen (M = 28 g mole ) at room temperature. If the average mass of a molecule of the gas in the container is g, the percent of oxygen in the container by mass is a. 5%. b. 25%. c. 50%. d. 75% e. 95%.

17 Chapter In order to calculate the pressure an ideal gas exerts on the wall of a container, we assume that each molecule transfers momentum of magnitude 2mv 0 xi when it collides with a wall perpendicular to the x-axis. We must also assume that the time interval between collisions in a cube of side length d is d a.. 2v xi d b.. v xi 2d c.. v xi d. 2d. v xi e. 2 2d v xi. 73. In order to calculate the pressure an ideal gas exerts on the wall of a container, we assume that each molecule transfers momentum of magnitude 2mv 0 xi when it collides with a wall perpendicular to the x-axis. We must also assume that the average value of v 2, v 2 2 is such that v x equals a. 1 3 b v. 2 v. c. v 2. d v. e. 3 2 v. 74. At a given temperature, the ratio of the root mean square speed of a molecule of hydrogen (M = 2gmole) to that of a molecule of oxygen (M = 32 g mole) is a. 1:4. b. 1:2. c. 1:1. d. 2:1. e. 4:1. ANS: e

18 312 Temperature and the Kinetic Theory of Gases 75. 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.