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In a Carnot engine operating between two heat reservoirs at temperatures 500 K a

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Question: In a Carnot engine operating between two heat reservoirs at temperatures 500 K and 300 K, what is the maximum efficiency of the engine? (2023)

Options:

  1. 40%
  2. 60%
  3. 80%
  4. 20%

Correct Answer: 60%

Exam Year: 2023

Solution: 

Efficiency (η) = 1 - (T_cold / T_hot) = 1 - (300 K / 500 K) = 0.4 or 40%.

In a Carnot engine operating between two heat reservoirs at temperatures 500 K a

Practice Questions

Q1
In a Carnot engine operating between two heat reservoirs at temperatures 500 K and 300 K, what is the maximum efficiency of the engine? (2023)
  1. 40%
  2. 60%
  3. 80%
  4. 20%

Questions & Step-by-Step Solutions

In a Carnot engine operating between two heat reservoirs at temperatures 500 K and 300 K, what is the maximum efficiency of the engine? (2023)
  • Step 1: Identify the temperatures of the two heat 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, which is 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%.
  • Carnot Efficiency – The maximum efficiency of a heat engine operating between two temperatures, derived from the second law of thermodynamics.
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