Question

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% 

• A. B and C only
• B. B and D only
• C. A and B only
• D. B, C and D only

Answer 1

The Correct Option is B

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.