In a Carnot engine operating between temperatures of 500 K and 300 K, what is th
Practice Questions
Q1
In a Carnot engine operating between temperatures of 500 K and 300 K, what is the efficiency of the engine? (2023)
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Questions & Step-by-Step Solutions
In a Carnot engine operating between temperatures of 500 K and 300 K, what is the efficiency of the engine? (2023)
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: Use the formula for the efficiency of a Carnot engine: Efficiency (η) = 1 - (T_cold / T_hot).
Step 3: Substitute the values into the formula: η = 1 - (300 K / 500 K).
Step 4: Calculate the fraction: 300 K / 500 K = 0.6.
Step 5: Subtract this value 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%.
