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NEET PHYSICSEasy

The efficiency of an ideal heat engine (Carnot heat engine) working between the freezing point and boiling point of water is:

A

26.80%

B

20%

C

6.25%

D

12.50%

Step-by-Step Solution

The efficiency (η\eta) of a Carnot engine is given by the formula: η=1T2T1\eta = 1 - \frac{T_2}{T_1} where T1T_1 is the temperature of the source (hot reservoir) and T2T_2 is the temperature of the sink (cold reservoir) in Kelvin.

  1. Identify Temperatures: Freezing point of water (T2T_2) = 0C=273.15 K273 K0^{\circ}\text{C} = 273.15 \text{ K} \approx 273 \text{ K}. Boiling point of water (T1T_1) = 100C=373.15 K373 K100^{\circ}\text{C} = 373.15 \text{ K} \approx 373 \text{ K}.

  2. Calculate Efficiency: η=1273373=373273373=100373\eta = 1 - \frac{273}{373} = \frac{373 - 273}{373} = \frac{100}{373} η0.268\eta \approx 0.268

  3. Convert to Percentage: Percentage Efficiency = 0.268×100%=26.8%0.268 \times 100\% = 26.8\%.

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