Unavailable Energy. The discussion of entropy and the

Chapter 20, Problem 20.57

(choose chapter or problem)

Unavailable Energy. The discussion of entropy and the second law that follows Example 20.10 (Section 20.7) says that the increase in entropy in an irreversible process is associated with energy becoming less available. Consider a Carnot cycle that uses a low-temperature reservoir with Kelvin temperature This is a true reservoirthat is, large enough not to change temperature when it accepts heat from the engine. Let the engine accept heat from an object of temperature where The object is of finite size, so it cools as heat is extracted from it. The engine continues to operate until (a) Show that the total magnitude of heat rejected to the low-temperature reservoir is where is the change in entropy of the high-temperature reservoir. (b) Apply the result of part (a) to 1.00 kg of water initially at a temperature of 373 K as the heat source for the engine and How much total mechanical work can be performed by the engine until it stops? (c) Repeat part (b) for 2.00 kg of water at 323 K. (d) Compare the amount of work that can be obtained from the energy in the water of Example 20.10 before and after it is mixed. Discuss whether your result shows that energy has become less available.