An engine operating between the boiling and freezing points of water will have
A. efficiency more than 27%
B. efficiency less than the efficiency a Carnot engine operating between the same two temperatures.
C. efficiency equal to 27%
D. efficiency less than 27%
An engine operating between the boiling and freezing points of water will have
A. efficiency more than 27%
B. efficiency less than the efficiency a Carnot engine operating between the same two temperatures.
C. efficiency equal to 27%
D. efficiency less than 27%
- B and C only
- B and D only
- A and B only
- B, C and D only
The Correct Option is B
Solution and Explanation
Solution:
The efficiency \( \eta \) of a Carnot engine is given by the formula:
\[
\eta = \left( 1 - \frac{T_2}{T_1} \right) \times 100
\]
where \( T_1 \) and \( T_2 \) are the temperatures of the hot and cold reservoirs in Kelvin.
For an engine operating between the freezing point (0°C) and the boiling point (100°C) of water:
\[
T_1 = 100 + 273 = 373 \, \text{K}, \quad T_2 = 0 + 273 = 273 \, \text{K}.
\]
Substituting these values into the formula:
\[
\eta = \left( 1 - \frac{273}{373} \right) \times 100 = 26.8\%.
\]
Thus, the efficiency of the engine is less than 27%, and the efficiency of the given engine will be less than the efficiency of a Carnot engine.
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