15.4 Exercise 8

Practical steam engines utilize $\text{450} º \text{C}$ steam, which is later exhausted at $\text{270} º \text{C}$. (a) What is the maximum efficiency that such a heat engine can have? (b) Since $\text{270} º \text{C}$ steam is still quite hot, a second steam engine is sometimes operated using the exhaust of the first. What is the maximum efficiency of the second engine if its exhaust has a temperature of $\text{150} º \text{C}$? (c) What is the overall efficiency of the two engines? (d) Show that this is the same efficiency as a single Carnot engine operating between $\text{450} º \text{C}$ and $\text{150} º \text{C}$. Explicitly show how you follow the steps in the Problem-Solving Strategies for Thermodynamics.