15.4 Carnot’s Perfect Heat Engine: The Second Law of Thermodynamics Restated

A certain gasoline engine has an efficiency of 30.0%. What would the hot reservoir temperature be for a Carnot engine having that efficiency, if it operates with a cold reservoir temperature of $2 \text{00} º \text{C}$?

(a) What is the hot reservoir temperature of a Carnot engine that has an efficiency of 42.0% and a cold reservoir temperature of $\text{27} . 0 º \text{C}$? (b) What must the hot reservoir temperature be for a real heat engine that achieves 0.700 of the maximum efficiency, but still has an efficiency of 42.0% (and a cold reservoir at $\text{27} . 0 º \text{C}$)? (c) Does your answer imply practical limits to the efficiency of car gasoline engines…

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?…

Would you be willing to financially back an inventor who is marketing a device that she claims has 25 kJ of heat transfer at 600 K, has heat transfer to the environment at 300 K, and does 12 kJ of work? Explain your answer.

Calculate the cold reservoir temperature of a steam engine that uses hot steam at $\text{450} º \text{C}$ and has a Carnot efficiency of 0.700. (b) What is unreasonable about the temperature? (c) Which premise is unreasonable?