# Energy in Thermal Processes: The First Law of Thermodynamics

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1 Energy in Thermal Processes: The First Law of Thermodynamics 1. An insulated container half full of room temperature water is shaken vigorously for two minutes. What happens to the temperature of the water? a. It increases. b. It decreases. c. It stays the same. d. It decreases by half. e. It doubles. 2. An insulated container half full of room temperature water is shaken vigorously for two minutes. What happens to the internal energy of the water? a. It increases. b. It decreases. c. It stays the same. d. It decreases by half. e. It doubles. 3. How many calories does a 66 kg woman use to climb a 2700 m high mountain? (1 cal = J) a b c d e

2 314 Energy in Thermal Processes: The First Law of Thermodynamics 4. A 150 lb. runner moving horizontally uses energy at the rate of 670 cal/lb/mile. How many calories would the runner need to run a 10 mile race? a b c d e What is the temperature in K of 1.0 kg of lead, initially at 300 K, after it falls 200 m? The specific heat of lead is 128 J kg C. a. 307 b. 311 c. 315 d. 275 e The temperature of 2.0 kg of water is 270 K. What is its temperature after falling 500 m? The specific heat of water is 4186 J kg C. a. 271 b. 269 c. 280 d. 275 e A kg copper cup is at 280 K. If J of energy is added to it, what is its final temperature in K. The specific heat of copper is 387 J kg C. a. 389 b. 392 c. 402 d. 409 e How many J are needed to raise kg of gold from 270 to 300 K? The specific heat of gold is 129 J kg C. a b c d e. 1950

3 Chapter A copper cup of mass kg contains 1.00 kg of water at 315 K. It is cooled so that the temperature decreases by 2.50 K each minute. What is the rate of removal of thermal energy in watts? The specific heat of water is 4186 J kg C and the specific heat of copper is 387 J kg C? a. 122 b. 185 c. 179 d. 162 e A 25 g lead bullet at 0 C moves at 375 m/s and strikes a block of ice at 0 C. What quantity of ice in kg is melted if all of the kinetic energy of the bullet is converted to heat? The block of ice does not move. (The latent heat of fusion of ice is 80 kcal/kg and the specific heat of lead is kcal kg C. 1 cal = J) a b c d e g of water at 100 K occupies a volume of 2. 5 cm 3 at atmospheric pressure. When the water is boiled, it occupies 4178 cm 3 as steam. What is the change in its internal energy? The latent heat of vaporization is J kg. The pressure of one atm is Nm 2. a b c d e Three moles of an ideal gas expand isothermally at 400 K to 3.0 times the initial volume. What is the work in J done by the gas if R = 831. J mol K? a b c d e

4 316 Energy in Thermal Processes: The First Law of Thermodynamics 13. A 100 kg student eats a 200 Calorie doughnut. How high in m would she have to climb to do that amount of work? (1 food Calorie = 10 3 calories. 1 cal = J) a. 273 b. 623 c. 418 d. 854 e A simple pendulum having a length of 2 meters and a mass of 5 kg is pulled 30 from the vertical and released. If it is allowed to swing until it comes to rest, how much energy in J is converted into thermal energy? a. 49 b. 63 c. 13 d. 17 e Gas in a container expands at a constant pressure of 3 atm. Find the work done in J by the gas if the initial volume is 5 liters and the final volume is 10 liters. (1 atm = Pa) a. 0 b. 150 c. 15 d. 1.5 e ANS: e 16. Gas in a container increases its pressure from 1 atm to 3 atm while keeping its volume constant. Find the work done in J by the gas if the volume is 5 liters. (R = 831. J mol K ) a b. 10 c d. 0 e In an adiabatic free expansion a. no heat is transferred between a system and its surroundings. b. the pressure remains constant. c. the temperature remains constant. d. the volume remains constant. e. the process is reversible.

5 Chapter In an isothermal process a. the volume remains constant. b. the temperature remains constant. c. no heat is transferred between a system and its surroundings. d. the pressure remains constant. e. the internal energy is not constant. 19. In an isobaric process a. the volume remains constant. b. the temperature remains constant. c. the pressure remains constant. d. no heat is transferred between a system and its surroundings. e. the internal energy is constant. 20. In an isovolumetric process a. the temperature remains constant. b. no heat is transferred between a system and its surroundings. c. the pressure remains constant. d. the volume remains constant. e. the internal energy is constant. 21. The work done in J by 5 moles of an ideal gas that is kept at 100 C in an expansion from 1 liter to 5 liters is (R = 831. J mol K ) a b c d e One gram of water is heated from 0 C to 100 C at a constant pressure of 1 atm. The approximate change in internal energy in cal of the water is a b c d e. 50.

6 318 Energy in Thermal Processes: The First Law of Thermodynamics 23. When kg of metal at 250 C is put into a calorimeter containing 0.41 kg of water at 25 C, the final temperature of the system is 30 C. What is the specific heat of the metal in J kg C? Ignore any thermal transfers between the calorimeter and its contents. The specific heat of water is 4186 J kg C. a. 453 b c. 765 d. 576 e The specific heat of silver is 234 J kg C. If a silver bullet of mass 4 g is shot into an insulating material with a speed of 300 m/s and comes to rest, what is the temperature increase of the bullet in C? a. 192 b. 47 c. 223 d e The heat capacity in calories/c of a lake containing one million gallons (approximately 4 million kilograms) of water is a b c d. insufficient information. e How many calories of heat are required to raise the temperature of 4 kg of water from 50 F to the boiling point? a b c d. 360 e A 5 gallon container of water (approximately 20 kg) having a temperature of 212 F is added to a 50 gallon tub (approximately 200 kg) of water having a temperature of 50 F. What is the final equilibrium temperature in C of the mixture? a. 54 b. 36 c. 18 d. 66 e. 14

7 Chapter A 5 kg piece of lead (specific heat 003. cal g C) having a temperature of 80 C is added to 500 g of water having a temperature of 20. What is the final equilibrium temperature in C of the system? a. 79 b. 26 c. 54 d. 34 e A 300 g solid glass cylinder initially at 25 C is put into 200 cm 3 of hot water at 95 C. Find the final temperature in C of the cylinder, assuming no heat flows to the surroundings. (The specific heat of glass is 02. cal g C.) a. 52 b. 68 c. 89 d. 79 e How much heat (in kilocalories) is needed to convert 1 kg of ice at 0 C into steam at 100 C? (L f = J kg; L v = J kg; 1 cal = J) a. 640 b. 180 c. 720 d. 360 e kg of ice at 0 C is combined with 4 kg of steam at 100 C. What is the final equilibrium temperature in C of the system? (L f = J kg; L v = J kg; 1 cal = J) a. 40 b. 20 c. 60 d. 100 e How much heat in kcal is needed to melt a 10 kg block of aluminum that has an initial temperature of 30 C? (The specific heat, latent heat of fusion, and melting point of aluminum are cal g C, 94.8 cal/g and 660 C.) a b c. 750 d. 430 e. 215

8 320 Energy in Thermal Processes: The First Law of Thermodynamics 33. How much heat in kcal must be removed from 2 kg of water at 20 C to make ice at 10 C? (The specific heat of ice is 05. cal g C.) (The heat of fusion of water is 80 cal/g.) a. 190 b. 200 c. 240 d. 210 e Five moles of an ideal gas expand isothermally at 100 C to five times its initial volume. Find the heat in J that flows into the system. (R = 831. J mol K ) a b c d e Two kg of water at 100 C is converted to steam at 1 atm. Find the work done in J. (The density of steam at 100 C is kg m 3. 1 atm = Pa.) a b c d e Two kg of water at 100 C is converted to steam at 1 atm. Find the change in internal energy in J. (1 atm = Pa; L v = J kg; 1 cal = J) a b c d e grams of liquid nitrogen at its boiling point of 77 K is stirred into a beaker containing 200 grams of 5.00 C water. If the nitrogen leaves the solution as soon as it turns to gas, how much water in g freezes? (The heat of vaporization of nitrogen is 48.0 cal/g and the heat of fusion of water is 79.6 cal/g.) a. 0 b. 48 c. 60 d. 114 e. 200

9 Chapter How much water in g at 20 C is needed to melt 1 kilogram of solid mercury at its melting point 39 C? (The heat of fusion of mercury is 2.80 cal/g. The specific heat of ice is cal g C and the heat of fusion of water is 79.6 cal/g.) a b c d e A styrofoam container used as a picnic cooler contains a block of ice at 0 C. If 225 grams of ice melts in 1 hour, how much heat energy per second in W is passing through the walls of the container? (The heat of fusion of ice is Jkg.) a b c d e In braking an automobile, the friction between the brake drums and brake shoes converts the car s kinetic energy into heat. If a 1500 kg automobile traveling at 30 m/s brakes to a halt, how much does the temperature rise in each of the four 8 kg brake drums? (The specific heat of each iron brake drum is 448 J kg C.) a. 42 C b. 44 C c. 47 C d. 49 C e. 51 C 41. A hot water heater is operated by using solar power. If the solar collector has an area of 6 m 2, and the power per unit area delivered by sunlight is 1000 W m 2, how long in hours will it take to increase the temperature of 1 m 3 of water from 20 C to 60 C? (1 cal = J) a. 2.1 b. 3.2 c. 7.8 d. 4.6 e. 4.1

10 322 Energy in Thermal Processes: The First Law of Thermodynamics 42. Two beakers of water are on the lab table. One beaker has 30 g of water at 80 C and the other has 80 g at 30 C. Which one would require more thermal energy to raise its temperature from 0 C to its present temperature? a. The 30 g beaker. b. The 80 g beaker. c. Both would require the same amount of thermal energy. d. Neither would require thermal energy to increase its temperature. e. We can t tell until we know the specific heat. 43. If the same amount of thermal energy is added to each of two different masses of water, a. the smaller mass of water will have the greater temperature increase. b. the larger mass of water will have the greater temperature increase. c. they both will have the same temperature increase. d. their temperature will not increase unless they are in contact. e. none of the above will happen. 44. Which of the following statements best describes the relationship between temperature and heat? a. They are the same. b. Heat is a measurement of temperature. c. The temperature of something shows how much heat it has. d. Temperature measures the effect of a heat transfer. e. Heat measures the effect of adding temperature. 45. A piece of apple pie produces 2650 calories when it is burned. What temperature change could it produce in 50 g of water if all the energy were transferred to the water? a. 53 C b. 266 C c. 15 C d. 75 C e. 50 C

11 Chapter A sample of water is heated at a constant rate through a certain temperature range without reaching the boiling point. Which of the graphs shows the temperature of the water as a function of the added heat? T T T T a. H T b. H c. H d. H e. H 47. One cup contains 100 g of water at 10 C and another 50 g of water at 70 C. What is the final temperature if the water in the two cups is mixed with no loss of heat? a. 30 C b. 40 C c. 50 C d. 60 C e. 11 C 48. The specific heat of liquid A, c A, is twice the specific heat of liquid B, c B. The same amount of thermal energy is added to equal masses of the two fluids at the same initial temperature. Compare the change in temperature of A, T A, with that of B, T B. a. TA = TB =0. b. TA = TB. c. TA = 2 TB. d. TB = 2 TA. e. 2 T = T. A B

12 324 Energy in Thermal Processes: The First Law of Thermodynamics 49. Energy transferred as a result of a temperature difference between two bodies is called a. heat. b. latent heat. c. specific heat capacity. d. work. e. internal energy. 50. In the PV diagram below, 2 moles of an ideal gas start in initial state a, double in volume at constant pressure, change pressure at constant volume, decrease in volume to the original volume and then return to the original pressure. The work done on the gas in J in process ab is P(Pa) 300 a b 100 a. 20. b c d e d c 3 V(m ) 51. In the PV diagram below, 2 moles of an ideal gas start in initial state a, double in volume at constant pressure, change pressure at constant volume, decrease in volume to the original volume and then return to the original pressure. The work done on the gas in J in process abcda is P(Pa) 300 a b 100 a. 20. b c d e d c 3 V(m )

13 52. A materials science engineer has produced a new material. To determine its specific heat in one experiment, she must measure a. its change in temperature T. b. the heat transfer to or from the material. c. the mass of the material. d. all of the above. e. only (a) and (b) above. Chapter One hundred J of energy is added to 1 kg quantities of iron, glass and water, each initially at the same temperature. c Fe = 448 J kg C; c Glass = 837 J kg C ; c Water = 4186 J kg C. Ranked in order from highest to lowest temperature after the energy transfer, they are a. water, glass, iron. b. water, iron, glass. c. glass, iron, water. d. glass, water, iron. e. iron, glass, water. ANS: e 54. A materials science engineer has produced a new material. To determine its latent heat of vaporization in one experiment, she must measure a. its change of temperature during vaporization. b. the heat transfer to the material. c. the mass of the material. d. all of the above. e. only (b) and (c) above. ANS: e 55. In an adiabatic free expansion, a gas isolated from its surroundings expands into an evacuated region. When an ideal gas comes to equilibrium after an adiabatic free expansion a. its temperature is lower than it was initially. b. its internal energy is lower than it was initially. c. the work done equals the work performed in a slow expansion to the same volume. d. all of the above are correct. e. its temperature and its internal energy are unchanged and no work has been performed. ANS: e 56. In a cyclic process, a. E int = 0. b. Q = W. c. T = 0. d. all of the above are correct. e. only (a) and (b) above are correct.

14 326 Energy in Thermal Processes: The First Law of Thermodynamics 57. The 0.75 cm thick windows of a house have a total surface area of 9. 0 m 2. The thermal conductivity of the single pane glass is 080. W m C. How much thermal energy in J does the home lose in 2 hours by heat conduction through its windows when the inside temperature is 22 C and the outside temperature is 4 C? a b c d e Thermal radiation from a naked human body at a normal body temperature of 37 C is greatest when that body is standing a. in an air cavity in a block of ice. b. outside when the temperature is 4 C. c. in a room that is at 22 C. d. in a cave in a desert when the temperature is 35 C. e. in the sun in a desert when the temperature is 35 C. 59. An astronaut working outside the space station loses thermal energy from her body principally through a. convection. b. radiation. c. convection and radiation. d. conduction and radiation. e. conduction, convection and radiation. 60. We are able to define a mechanical equivalent for heat because a. some thermal energy can be converted into mechanical energy. b. mechanical energy can be converted into thermal energy. c. work can be converted into thermal energy. d. some thermal energy can be converted into work. e. all of the above can occur. ANS: e. 61. A 72 kg student wins a bet by eating kcal jelly doughnuts. How many times must he run up the steps from the basement to the twelfth floor of his dorm, 33 m above the basement, in order to work off the extra calories? (1 cal = J) Only count going up, not going back down, in your calculation. a. 135 b. 405 c. 809 d e. 2427

15 Chapter A physicist wants to place a kg block of beryllium, initially at 20 C, in a neutron beam in order to obtain cold neutrons. She wants to use liquid nitrogen to cool the block to 196 C, the boiling point of liquid nitrogen. If the specific heat of beryllium is 1, 830 J kg C, and the latent heat of liquid nitrogen is J kg, what mass of liquid nitrogen in kg is needed just to cool the beryllium down to 196 C? a b c d e Let m c, c c and T c represent the mass, specific heat, and temperature of a cold substance. Let m h, c h and T h represent the mass, specific heat, and temperature of a hot substance. When a cold solid is immersed in a hot liquid, or a hot solid is immersed in a cold liquid, the equation we can always derive from conservation of energy principles is a. mcccbt+ Tcg= mc h hbt+ Thg. b.mcccbt Tcg= mc h hbt+ Thg. c. mcccbt+ Tcg= mc h hbt Thg. d. mcccbt Tcg= mc h hbt Thg. e. mc T T = mc T T ANS: e b g b g. c c c h h h 64. In the PV-diagram below, 2 moles of an ideal gas start in initial state a, double in volume at constant pressure, change pressure at constant volume, decrease in volume to the original volume and then return to the original pressure. The change in internal energy of the gas in J in the process abcda is P(Pa) 300 a b 100 a. 40. b. 20. c. 0. d e d c 3 V(m )

16 328 Energy in Thermal Processes: The First Law of Thermodynamics 65. To calculate the work done on an ideal gas in an isothermal process, we must use dw = PdV and set a. V = nrt. P b. T = PV. nr c. P nrt =. V V d. P =. nrt P e. V =. nrt 66. Both Q and E int are positive when a. water is shot out of a water gun. b. a bicycle is used to pump up a child s plastic swimming pool. c. clear soup is heated on a hot stove. d. a volume of air is cooled by an air conditioner. e. ice cubes form from water in a freezer. 67. In an isothermal process a. P is constant. b. V is constant. c. P is constant. T d. PV is constant. e. V is constant. n 68. The specific heat of an ideal gas at constant pressure is greater than the specific heat of an ideal gas at constant volume because a. work is done by a gas at constant pressure. b. work is done by a gas at constant volume. c. no work is done by a gas at constant pressure. d. the temperature remains constant for a gas at constant pressure. e. the temperature remains constant for a gas at constant volume. 69. In the initial stages of liquefaction of air, a compressor reduces the volume of 1000 cm 3 of air to 100 cm 3. If γ = 140. for air, before any heat is transferred to the surroundings, the pressure in the gas in atm is a b c d e

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