Question: A heat engine operates using the following cycle: reversible isothermal expansion at a temperature of 400 K, reversible adiabatic expansion, reversible isothermal compression at a temperature of 300 K, and reversible adiabatic compression. Calculate the thermal efficiency of this heat engine.

Answer: The thermal efficiency of a heat engine is given by the formula:

Where:

• $\eta$ = thermal efficiency
• $T_C$ = temperature of the cold reservoir
• $T_H$ = temperature of the hot reservoir

First, we need to determine the temperatures of the reservoirs during the cycle. According to the Carnot cycle, the temperatures of the hot and cold reservoirs can be determined using the formula:

Where:

• $Q_H$ = heat absorbed from the hot reservoir
• $Q_C$ = heat rejected to the cold reservoir

Since this is a Carnot cycle, both the isothermal processes are reversible, and the adiabatic processes are reversible, so the efficiency is given by the equation above.

Given: $T_H = 400$ K $T_C = 300$ K

Using the above information, the equation for thermal efficiency becomes:

Therefore, the thermal efficiency of this heat engine is 25%.