Physics A



Physics A

Chapter 9 - Heat

1) The Westin Stamford Hotel in Detroit is 228 m tall. Suppose a piece of ice, which initially has a temperature of 0(C, falls from the hotel roof and crashes to the ground. Assuming that 50% of the ice’s mechanical energy during the fall and collision is absorbed by the ice and that 3.33 ( 105 J is required to melt 1.00 kg of ice, calculate the fraction of the ice’s mass that would melt.

2) The French-built Concorde, the fastest passenger jet plane, is known to travel with a speed as great as 2,333 km/h (about 650 m/s). Suppose the plane travels horizontally at an altitude of 4000 m and at maximum speed when a fragment of metal breaks free from the plane. The metal has, of course, the same horizontal speed as the plane, and when it lands on the ground, it will have absorbed 1% of its total mechanical energy. If it takes 355 J to raise the temperature of 1.00 kg of this metal by 1.00(C, how great a temperature change will the metal fragment experience from the time it breaks free from the Concorde to the time it lands on the ground? Ignore air resistance.

3) Angel Falls, the highest waterfall in the world, is located in Venezuela. Estimate the height of the waterfall, assuming that the water that falls the complete distance experiences a temperature increase of 0.23(C. Assume that the water absorbs 10% of its mechanical energy and that 4186 J is needed to raise the temperature of 1 kg of water by 1(C.

4) In 1992, the average rate of energy consumption in the United States was about 2.8 ( 109 W. Suppose all of the copper produced in the United States in 1992 is placed in the giant calorimeter used in the sample problem. The quantity of energy transferred by heat from the copper to the water is equal to the energy used in the United States during 1.2 s of 1992. If the initial temperature of the copper is 26.0(C, and the final temperature is 21.0(C, what is the mass of the copper?

5) In 1994, to commemorate the 200th anniversary of a beverage company, a giant bottle was constructed and filled with 2,250 kg of the company’s lemonade. Suppose the lemonade has an initial temperature of 28(C when 900 kg of ice with a temperature of (18(C is added to it. What is the lemonade’s temperature at the moment the temperature of the ice reaches 0(C? Assume that the lemonade has the same specific heat capacity as water.

6) The water in the Arctic Ocean has a total mass of 1.33 ( 1019 kg. The average temperature of the water is estimated to be 4.000(C. What would the temperature of the water in the Arctic Ocean be if the energy produced in 1000 years by the world’s largest power plant (1.33 ( 1010 W) were transferred by heat to it?

7) Lake Superior contains about 1.20 ( 1016 kg of water, whereas Lake Erie contains only 4.8 ( 1014 kg of water. Suppose aliens use these two lakes for cooking. They heat Lake Superior to 100(C and freeze Lake Erie to 0(C. Then they mix the two lakes together to make a “lake shake.” What would be the final temperature of the mixture? Assume that the entire energy transfer by heat occurs between the lakes.

8) The lowest temperature measured on the surface of a planetary body in the solar system is that of Triton, the largest of Neptune’s moons. The surface temperature on this distant moon can reach a low of (235(C. Suppose an astronaut brings a water bottle containing 0.500 kg of water to Triton. The water’s temperature decreases until the water freezes, then the temperature of the ice decreases until it is in thermal equilibrium with Triton at a temperature of (235(C. If the energy transferred by heat from the water to Triton is 471 kJ, what is the value of the water’s initial temperature?

9) The United States Bullion Depository at Fort Knox, Kentucky, contains almost half a million standard mint gold bars, each with a mass of 12.4414 kg. Assuming an initial bar temperature of 5.0(C, each bar will melt if it absorbs 2.50 MJ of energy transferred by heat. If the specific heat capacity of gold is 129 J/kg((C and the melting point of gold is 1063(C, calculate the heat of fusion of gold.

Physics A

Chapter 10 - Thermodynamics

1) The largest glass bottle made by the method of glass-blowing was over 2 m tall. Suppose the net pressure used to expand the bottle to full volume was 5,100 Pa. If 3,600 J of work was done in expanding the bottle from an initial volume of 0 m3, what was the final volume?

2) Nicholas Mason inflated a weather balloon using just the power of his lungs. The balloon’s final radius was

1.22 m. If 642 kJ of work was done to inflate the balloon, at what net pressure was the balloon inflated?

3) Susan Williams, of California, blew a bubble-gum bubble with a radius of 29.2 cm. If this were done with a constant net pressure of 25.0 kPa, the work done could have been used to launch a model airplane. If the airplane’s mass was 160.0 g, what would have been the launch speed?

4) An average elephant has a mass of 5000 kg. Contrary to popular belief, elephants are not slow; they can achieve speeds of up to 40.0 km/h. Imagine a sample of gas that does an amount of work equal to the work required for an average elephant to move from rest to its maximum speed. If the initial internal energy of the gas, 2.50 ( 105 J, is to be doubled, how much energy must be transferred to the gas by heat?

5) The rate of nuclear energy production in the United States in 1992 was about 5.9 ( 109 J/s. Suppose one second’s worth of this energy is transferred by heat to an ideal gas. How much work must be done on or by this gas so that the net increase in its internal energy is 2.6 ( 109 J?

6) The oldest working steam engine was designed in 1779 by James Watt. Suppose this engine’s efficiency is

8%. How much energy must be transferred by heat to the engine’s surroundings if 2,500 J is transferred by heat into the engine? How much work is done?

7) A steam engine built in 1812 still works at its original site in England. The engine delivers 19 kW of net power. If the engine’s efficiency is 6%, how much energy must be transferred by heat to the engine in 1 hour?

8) The world’s tallest mobile crane can lift 3.00 ( 104 kg to a height of 1.60 ( 102 m. What is the efficiency of a heat engine that does the same task while losing 3.60 ( 108 J of energy by heat to the surroundings?

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Answers to Chapter 9: 1) fraction that melts is 3.4 x 10-3 2) 7.04Ú[?]C 3) 963 m 4) 1.7 x 106 kg 5) 24.4Ú[?]C 6) 4.008Ú[?]C 7) 92.9Ú[?]C 8) 28Ú[?]C

7.04˚C 3) 963 m 4) 1.7 x 106 kg 5) 24.4˚C 6) 4.008˚C 7) 92.9˚C 8) 28˚C

9) 64,000 J/kg

Answers to Chapter 10: 1) 0.71 m3 2) 8.44 x 104 Pa 3) 181 m/s 4) 5.59 x 105 J 5) 3.3 x 109 J 6) Qcold = 2,300 J; W = 200 J 7) 1.1 x 109 J 8) 12%

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