Step 1: Identify the temperatures of the hot and cold reservoirs. The hot reservoir temperature (T_hot) is 500 K and the cold reservoir temperature (T_cold) is 300 K.
Step 2: Write down the formula for the efficiency of a Carnot engine: Efficiency (η) = 1 - (T_cold / T_hot).
Step 3: Substitute the values of T_cold and T_hot into the formula: η = 1 - (300 K / 500 K).
Step 4: Calculate the fraction: 300 K / 500 K = 0.6.
Step 5: Subtract this fraction from 1: η = 1 - 0.6.
Step 6: Calculate the result: η = 0.4.
Step 7: Convert the efficiency to a percentage: 0.4 = 40%.
