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Question:

The efficiency of an ideal heat engine working between the freezing point and boiling point of water, is?

6.25

12.5

26.8

20

Solution:

The efficiency of an ideal heat engine is given by the formula:

η = 1 - (T_c / T_h)

where:

  • η is the efficiency of the heat engine
  • T_c is the absolute temperature of the cold reservoir (freezing point of water)
  • T_h is the absolute temperature of the hot reservoir (boiling point of water)

The freezing point of water is 0°C or 273.15 K.
The boiling point of water is 100°C or 373.15 K.

Substituting these values into the formula:

η = 1 - (273.15 K / 373.15 K)

η = 1 - 0.732

η ≈ 0.268

Converting this to a percentage:

η ≈ 0.268 * 100% = 26.8%

Therefore, the efficiency of an ideal heat engine working between the freezing point and boiling point of water is approximately 26.8%. The correct option is 26.8