Question:
The efficiency of Carnot engine which operates between the two temperatures \(T_1 = 500\) K and \(T_2 = 300\) K is
The efficiency of Carnot engine which operates between the two temperatures \(T_1 = 500\) K and \(T_2 = 300\) K is
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Carnot efficiency is 1 minus the ratio of the sink temperature to the source temperature.
Updated On: Oct 1, 2026
- \(75 \%\)
- \(50 \%\)
- \(25 \%\)
- \(40 \%\)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
The efficiency of a Carnot engine depends only on the temperatures of the hot source and the cold sink, both in kelvin.
Step 2: Key Formula or Approach
\[ \eta=1-\frac{T_2}{T_1} \]
Step 3: Substitute
\[ \eta=1-\frac{300}{500}=1-0.6=0.4 \]
\[ \eta=40\% \]
Step 4: Check the options
75% would need the sink at 125 K. 50% needs a sink at 250 K. 25% needs a sink at 375 K. Only 40% matches 300 K, option (D).
Final Answer:
The efficiency is 1 - 300/500 = 40 percent, option (D). \[ \boxed{40\%} \]
The efficiency of a Carnot engine depends only on the temperatures of the hot source and the cold sink, both in kelvin.
Step 2: Key Formula or Approach
\[ \eta=1-\frac{T_2}{T_1} \]
Step 3: Substitute
\[ \eta=1-\frac{300}{500}=1-0.6=0.4 \]
\[ \eta=40\% \]
Step 4: Check the options
75% would need the sink at 125 K. 50% needs a sink at 250 K. 25% needs a sink at 375 K. Only 40% matches 300 K, option (D).
Final Answer:
The efficiency is 1 - 300/500 = 40 percent, option (D). \[ \boxed{40\%} \]
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