A cyclic heat engine operates between a source temperature of 727°C and a sink temperature of 27°C. Maximum efficiency of the engine is _________.

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SSC JE Mechanical 14 Nov 2022 Shift 2 Official Paper
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  1. 70%
  2. 42.85%
  3. 30%
  4. 23.33%

Answer (Detailed Solution Below)

Option 1 : 70%
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Detailed Solution

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Concept:

For the maximum efficiency of the heat engine,  the heat engine cycle should reject the least rate of heat (QL) which is only possible when it operates on the Carnot cycle.

For maximum efficiency of  heat engines,

\(η = \frac{W}{{{Q_H}}} = \frac{{{T_H} - {T_L}}}{{{T_H}}} = 1 - \frac{{{T_L}}}{{{T_H}}}\)

Calculation:

Given TH =  727°C = 1000 K, TL = 27°C = 300 K

\(η = 1 - \frac{{{T_L}}}{{{T_H}}} = 1 - \frac{{300}}{{1000}}\)

η = 0.70 = 70%

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