# Physics Assignment No 2 Chapter 20 The First Law of Thermodynamics Note: Answers are provided only to numerical problems.

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1 Serway/Jewett: PSE 8e Problems Set Ch Physics Assignment No 2 Chapter 20 The First Law of Thermodynamics Note: Answers are provided only to numerical problems. 1. How long would it take a W heater to melt 1.00 kg of ice at 20.0 C, assuming all the energy from the heater is absorbed by the ice? (a) 4.18 s (b) 41.8 s (c) 5.55 min (d) 6.25 min (e) 38.4 min 2. A 100-g piece of copper, initially at 95.0 C, is dropped into 200 g of water contained in a 280-g aluminum can; the water and can are initially at 15.0 C. What is the final temperature of the system? (Specific heats of copper and aluminum are and cal/g C, respectively.) (a) 16 C (b) 18 C (c) 24 C (d) 26 C (e) none of those answers 3. The specific heat of substance A is greater than that of substance B. Both A and B are at the same initial temperature when equal amounts of energy are added to them. Assuming no melting or vaporization occurs, which of the following can be concluded about the final temperature T A of substance A and the final temperature T B of substance B? (a) T A > T B (b) T A < T B (c) T A = T B (d) More information is needed.

2 Serway/Jewett: PSE 8e Problems Set Ch An amount of energy is added to ice, raising its temperature from 10 C to 5 C. A larger amount of energy is added to the same mass of water, raising its temperature from 15 C to 20 C. From these results, what would you conclude? (a) Overcoming the latent heat of fusion of ice requires an input of energy. (b) The latent heat of fusion of ice delivers some energy to the system. (c) The specific heat of ice is less than that of water. (d) The specific heat of ice is greater than that of water. (e) More information is needed to draw any conclusion. 5. How much energy is required to raise the temperature of 5.00 kg of lead from 20.0 C to its melting point of 327 C? The specific heat of lead is 128 J/kg C. (a) J (b) J (c) J (d) J (e) J 6. Ethyl alcohol has about one-half the specific heat of water. Assume equal amounts of energy are transferred by heat into equal-mass liquid samples of alcohol and water in separate insulated containers. The water rises in temperature by 25 C. How much will the alcohol rise in temperature? (a) It will rise by 12 C. (b) It will rise by 25 C. (c) It will rise by 50 C. (d) It depends on the rate of energy transfer. (e) It will not rise in temperature.

3 Serway/Jewett: PSE 8e Problems Set Ch Assume you are measuring the specific heat of a sample of originally hot metal by using a calorimeter containing water. Because your calorimeter is not perfectly insulating, energy can transfer by heat between the contents of the calorimeter and the room. To obtain the most accurate result for the specific heat of the metal, you should use water with which initial temperature? (a) slightly lower than room temperature (b) the same as room temperature (c) slightly higher than room temperature (d) whatever you like because the initial temperature makes no difference 8. Beryllium has roughly one-half the specific heat of water (H 2 O). Rank the quantities of energy input required to produce the following changes from the largest to the smallest. In your ranking, note any cases of equality. (a) raising the temperature of 1 kg of H 2 O from 20 C to 26 C (b) raising the temperature of 2 kg of H 2 O from 20 C to 23 C (c) raising the temperature of 2 kg of H 2 O from 1 C to 4 C (d) raising the temperature of 2 kg of beryllium from 1 C to 2 C (e) raising the temperature of 2 kg of H 2 O from 1 C to 2 C (e >a=b-c>d) 9. A person shakes a sealed insulated bottle containing hot coffee for a few minutes. (i) What is the change in the

4 Serway/Jewett: PSE 8e Problems Set Ch temperature of the coffee? (a) a large decrease (b) a slight decrease (c) no change (d) a slight increase (e) a large increase (ii) What is the change in the internal energy of the coffee? Choose from the same possibilities. 10. A poker is a stiff, nonflammable rod used to push burning logs around in a fireplace. For safety and comfort of use, should the poker be made from a material with (a) high specific heat and high thermal conductivity, (b) low specific heat and low thermal conductivity, (c) low specific heat and high thermal conductivity, or (d) high specific heat and low thermal conductivity? 11. Star A has twice the radius and twice the absolute surface temperature of star B. The emissivity of both stars can be assumed to be 1. What is the ratio of the power output of star A to that of star B? (a) 4 (b) 8 (c) 16 (d) 32 (e) If a gas is compressed isothermally, which of the following statements is true? (a) Energy is transferred into the gas by heat. (b) No work is done on the gas. (c) The temperature of the gas increases. (d) The internal energy of the gas remains

5 Serway/Jewett: PSE 8e Problems Set Ch constant. (e) None of those statements is true. 13. When a gas undergoes an adiabatic expansion, which of the following statements is true? (a) The temperature of the gas does not change. (b) No work is done by the gas. (c) No energy is transferred to the gas by heat. (d) The internal energy of the gas does not change. (e) The pressure increases. 14. If a gas undergoes an isobaric process, which of the following statements is true? (a) The temperature of the gas doesn t change. (b) Work is done on or by the gas. (c) No energy is transferred by heat to or from the gas. (d) The volume of the gas remains the same. (e) The pressure of the gas decreases uniformly. 15. An ideal gas is compressed to half its initial volume by means of several possible processes. Which of the following processes results in the most work done on the gas? (a) isothermal (b) adiabatic (c) isobaric (d) The work done is independent of the process.

6 Serway/Jewett: PSE 8e Problems Set Ch Practice Problems (Students are encourage to Practice these problems, need not submit) 3. A combination of kg of water at 20.0 C, kg of aluminum at 26.0 C, and kg of copper at 100 C is mixed in an insulated container and allowed to come to thermal equilibrium. Ignore any energy transfer to or from the container. What is the final temperature of the mixture? ANS: What mass of water at 25.0 C must be allowed to come to thermal equilibrium with a 1.85-kg cube of aluminum initially at 150 C to lower the temperature of the aluminum to 65.0 C? Assume any water turned to steam subsequently condenses. ANS: An aluminum cup of mass 200 g contains 800 g of water in thermal equilibrium at 80.0 C. The combination of cup and water is cooled uniformly so that the temperature decreases by 1.50 C per minute. At what rate is energy being removed by heat? Express your answer in watts. ANS: 88.2 W 13. Two thermally insulated vessels are connected by a narrow tube fitted with a valve that is initially closed as shown in Figure P One vessel of volume 16.8 L contains oxygen at a

7 Serway/Jewett: PSE 8e Problems Set Ch temperature of 300 K and a pressure of 1.75 atm. The other vessel of volume 22.4 L contains oxygen at a temperature of 450 K and a pressure of 2.25 atm. When the valve is opened, the gases in the two vessels mix and the temperature and pressure become uniform throughout. (a) What is the final temperature? (b) What is the final pressure? ANS: a) 389 K b) 2.04 atm 16. A 3.00-g lead bullet at 30.0 C is fired at a speed of 240 m/s into a large block of ice at 0 C, in which it becomes embedded. What quantity of ice melts? ANS: g 17. Steam at 100 C is added to ice at 0 C. (a) Find the amount of ice melted and the final temperature when the mass of steam is 10.0 g and the mass of ice is 50.0 g. (b) What If? Repeat when the mass of steam is 1.00 g and the mass of ice is 50.0 g. ANS: a) 40.4 o C

8 Serway/Jewett: PSE 8e Problems Set Ch A 1.00-kg block of copper at 20.0 C is dropped into a large vessel of liquid nitrogen at 77.3 K. How many kilograms of nitrogen boil away by the time the copper reaches 77.3 K? (The specific heat of copper is cal/g C, and the latent heat of vaporization of nitrogen is 48.0 cal/g.) ANS: kg 21. An ideal gas is enclosed in a cylinder with a movable piston on top of it. The piston has a mass of g and an area of 5.00 cm 2 and is free to slide up and down, keeping the pressure of the gas constant. How much work is done on the gas as the temperature of mol of the gas is raised from 20.0 C to 300 C? ANS: -466 J 23. An ideal gas is taken through a quasi-static process described by P = αv 2, with α = 5.00 atm/m 6, as shown in Figure P The gas is expanded to twice its original volume of 1.00 m 3. How much work is done on the expanding gas in this process? ANS: MJ

9 Serway/Jewett: PSE 8e Problems Set Ch (a) Determine the work done on a gas that expands from i to f as indicated in Figure P (b) What If? How much work is done on the gas if it is compressed from f to i along the same path? ANS: a) J b)12 MJ 31. An ideal gas initially at 300 K undergoes an isobaric expansion at 2.50 kpa. If the volume increases from 1.00 m 3 to 3.00 m 3 and 12.5 kj is transferred to the gas by heat, what are (a) the change in its internal energy and (b) its final temperature? ANS: a) 7.50 kj b) 900 K 34. One mole of an ideal gas does J of work on its surroundings as it expands isothermally to a final pressure of 1.00 atm and volume of 25.0 L. Determine (a) the initial volume and (b) the temperature of the gas. ANS: 305 K 40. A concrete slab is 12.0 cm thick and has an area of 5.00 m 2.

10 Serway/Jewett: PSE 8e Problems Set Ch Electric heating coils are installed under the slab to melt the ice on the surface in the winter months. What minimum power must be supplied to the coils to maintain a temperature difference of 20.0 C between the bottom of the slab and its surface? Assume all the energy transferred is through the slab. ANS: 667 W 47. (a) Calculate the R-value of a thermal window made of two single panes of glass each in. thick and separated by a in. air space. (b) By what factor is the transfer of energy by heat through the window reduced by using the thermal window instead of the single-pane window? Include the contributions of inside and outside stagnant air layers. ANS: a) 1.85 ft 2.F.h/Btu b) A bar of gold (Au) is in thermal contact with a bar of silver (Ag) of the same length and area (Fig. P20.49). One end of the compound bar is maintained at 80.0 C, and the opposite end is at 30.0 C. When the energy transfer reaches steady state, what is the temperature at the junction?

11 ANS:51.2 o C Serway/Jewett: PSE 8e Problems Set Ch

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