23. The Second Law of Thermodynamics

(III) A Carnot cycle, shown in Fig. 20–5, has the following conditions: V_a = 7.5 L, V_b = 15.0 L, T_H = 470°C and T_L = 260°C. The gas used in the cycle is 0.50 mol of a diatomic gas, γ = 1.4. Calculate the pressures at a and b.

A Carnot engine is operated between two heat reservoirs at temperatures of $520$ K and $300$ K. If the engine receives $6.45$ kJ of heat energy from the reservoir at $520$ K in each cycle, how many joules per cycle does it discard to the reservoir at $300$ K?

A Carnot engine with an efficiency of 70% is cooled by water at 10°C. What temperature must the hot reservoir be maintained at?

At what cold-reservoir temperature (in ℃) would a Carnot engine with a hot-reservoir temperature of 427℃ have an efficiency of 60%?

A Carnot heat engine operates between reservoirs at 182℃ and 0℃. If the engine extracts 25 J of energy from the hot reservoir per cycle, how many cycles will it take to lift a 10 kg mass a height of 10 m?

The engine that powers a crane burns fuel at a flame temperature of 2000℃. It is cooled by 20℃ air. The crane lifts a 2000 kg steel girder 30 m upward. How much heat energy is transferred to the engine by burning fuel if the engine is 40% as efficient as a Carnot engine?

A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. In $5$ minutes of operation, the heat rejected by the engine melts $0.0400$ kg of ice. During this time, how much work $W$ is performed by the engine?

A Carnot engine whose hot-reservoir temperature is 400℃ has a thermal efficiency of 40%. By how many degrees should the temperature of the cold reservoir be decreased to raise the engine's efficiency to 60%?