Question:medium
The efficiency of an ideal heat engine working between the freezing point and boiling point of water, is
The efficiency of an ideal heat engine working between the freezing point and boiling point of water, is
Updated On: Apr 23, 2026
- 26.8%
- 6.25%
- 20%
- 12.5%
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The Correct Option is A
Solution and Explanation
The question requires us to determine the efficiency of an ideal heat engine working between the freezing point and boiling point of water. The Carnot efficiency is given by:
\[ \eta = 1 - \frac{T_C}{T_H} \]
where:
- \( T_H \) is the absolute temperature (in Kelvin) of the hot reservoir.
- \( T_C \) is the absolute temperature (in Kelvin) of the cold reservoir.
The boiling point of water is \( 100^\circ\text{C} = 373\,\text{K} \).
The freezing point of water is \( 0^\circ\text{C} = 273\,\text{K} \).
Substituting these values:
\[ \eta = 1 - \frac{273}{373} \]
\[ \frac{273}{373} \approx 0.7311 \]
\[ \eta = 1 - 0.7311 = 0.2689 \]
Converting to percentage:
\[ \eta \approx 26.89\% \]
Rounding to one decimal place:
\( \eta \approx 26.8\% \)
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