Question:
The efficiency of a Carnot engine using an ideal gas as the working substance is given by which of the following equation ?
The efficiency of a Carnot engine using an ideal gas as the working substance is given by which of the following equation ?
Show Hint
Carnot efficiency can never be \( 100\% \) unless the sink temperature \( T_2 \) is absolute zero (\( 0\text{ K} \)), which is physically impossible.
Updated On: Jul 21, 2026
- \( \frac{T_1}{T_1 - T_2} \)
- \( \frac{T_1 - T_2}{T_1} \)
- \( \frac{T_2(T_1 - T_2)}{T_1(T_1 - T_2)} \)
- \( \frac{T_1 T_2}{T_1 - T_2} \)
Show Solution
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
The Carnot cycle is an idealized thermodynamic cycle that provides the maximum possible efficiency for a heat engine operating between two temperatures.
Key Formula or Approach:
The efficiency (\( \eta \)) of a Carnot engine is determined solely by the absolute temperatures of the heat source (\( T_1 \)) and the heat sink (\( T_2 \)):
\[ \eta = 1 - \frac{T_2}{T_1} \]
Step 2: Detailed Explanation:
Let us simplify the efficiency formula:
\[ \eta = 1 - \frac{T_2}{T_1} = \frac{T_1 - T_2}{T_1} \]
where:
\( T_1 \) is the absolute temperature of the source (hot reservoir),
\( T_2 \) is the absolute temperature of the sink (cold reservoir).
This indicates that the efficiency depends only on the temperature difference relative to the source temperature.
This matches option 2.
Step 3: Final Answer:
The efficiency of a Carnot engine is given by \( \frac{T_1 - T_2}{T_1} \).
The Carnot cycle is an idealized thermodynamic cycle that provides the maximum possible efficiency for a heat engine operating between two temperatures.
Key Formula or Approach:
The efficiency (\( \eta \)) of a Carnot engine is determined solely by the absolute temperatures of the heat source (\( T_1 \)) and the heat sink (\( T_2 \)):
\[ \eta = 1 - \frac{T_2}{T_1} \]
Step 2: Detailed Explanation:
Let us simplify the efficiency formula:
\[ \eta = 1 - \frac{T_2}{T_1} = \frac{T_1 - T_2}{T_1} \]
where:
\( T_1 \) is the absolute temperature of the source (hot reservoir),
\( T_2 \) is the absolute temperature of the sink (cold reservoir).
This indicates that the efficiency depends only on the temperature difference relative to the source temperature.
This matches option 2.
Step 3: Final Answer:
The efficiency of a Carnot engine is given by \( \frac{T_1 - T_2}{T_1} \).
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