Heat Engines, Entropy, & the Second Law

Homework Assignment

Chapter 22:

Questions 22:3, 4, 6, 16, 17

Problems 22:1, 2, 6, 7, 8, 9, 11, 28, 31, 32, 41

Be sure and do these; do not just wait and watch me do them in class!

Course calendar | Homework Solutions |

Q22.3 Use the first law of thermodynamics to explain why the total energy of an isolated system is always constant.

Q22.4 Is it possible toonvert internal energy to mechanical energy?

!22.6 In practical heat engines, which do we have more control of, the temperature of the hot reservoir or the temperature of the cold reservoir? Explain.

Q22.16 Give an example of a process in nature that is nearly reversible.

Q22.17 A thermodynamic process occurs in which the entropy of the system changes by - 8.0 J/K. According to the second law of thermodynamics, what can you conclude about the entropy change of the environment?

22.1 A heat engine absorbs 360 J of thermal energy and performs 25 J of work in each cycle.

Find (a) the efficiency of the engine

and (b) the thermal energy expelled in each cycle.

22.2 A heat engine performs 200 J of work in each cycle and has an efficiency of 30%. For each cycle, how much thermal energy is

(a) absorbed and

(b) expelled?

22.6 A particular engine has a power output of 5.0 kW and an efficiency of 25%. If the engine expels 8 000 J of thermal energy in each cycle, find

(a0 the heat absorbed in each cycle and

(b) the time for each cycle.

22.7 An engine absorbs 1 600 J from a hot reservoir and expels 1 000 J to a cold reservoir in each cycle.

(a) What is the efficiency of the engine?

(b) What is the power output of the engine if each cycle lasts for 0.30 s?

22.8 A heat engine operates between two reservoirs at 20oC and 300oC. What is the maximum efficiency possible for this engine?

22.9 A power plant operates at a 32% efficiency during the summer when the sea water for cooling is at 20oC. The plant uses 350oC steam to drive turbines. Assuming the plant's efficiency changes in the same proportion as the ideal efficiency, what is the plant's efficiency in the winter when the sea water is at 10oC?

22.11 A power plant has been proposed that would make use of thetemperature gradient in the ocean. The system is to operate between 20oC (surface water temperature) and 5oC (water temperature at a depth of about 1 km).

(a) What is the maximum efficiency of such a ssystem?

(b) If the power output of the plant is 75MW, how much thermal energy is absorbed per hour?

(c) What compensating factor made this proposal of interest despite the value of the efficiency calculated in part (a)?

22.14 Steam enters a turbine at 800oC and is exhausted at 120oC. What is the maximum efficiency of this turbine?

22.28 What is the change in entropy when 1 mole of silver (108 g) is melted at 961oC?

22.31 Calculate the change in entropy of 250 g of water heated slowly from 20oC to 80oC.

(Hint: Note that dQ = m c dT).

22.32 An ice tray contains 500 g of water at 0oC. Calculate thechange in entropy of the water as it freezes completely and slowly at 0oC.

22.41 An 18-g ice cube at 0.0ooC is heated until it vaporizes as steam.

(a) How much does the entropy increase?

(See Table 20.2)

(b) How much energy was required to vaporize the ice cube?


Heat Engines

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(c) Doug Davis, 2002; all rights reserve