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In a Carnot engine operating between temperatures of 500 K and 300 K, what is th
In a Carnot engine operating between temperatures of 500 K and 300 K, what is the maximum efficiency? (2023)
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In a Carnot engine operating between temperatures of 500 K and 300 K, what is the maximum efficiency? (2023)
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Efficiency (η) = 1 - (T_cold / T_hot) = 1 - (300 K / 500 K) = 0.4 or 40%.
Questions & Step-by-step Solutions
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Q
Q: In a Carnot engine operating between temperatures of 500 K and 300 K, what is the maximum efficiency? (2023)
Solution:
Efficiency (η) = 1 - (T_cold / T_hot) = 1 - (300 K / 500 K) = 0.4 or 40%.
Steps: 7
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Step 1: Identify the temperatures involved in the Carnot engine. The hot temperature (T_hot) is 500 K and the cold temperature (T_cold) is 300 K.
Step 2: Use the formula for 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%.
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