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Question
A Carnot engine whose efficiency is 45% takes heat from a source maintained at a temperature of 327°C. To have an engine of efficiency of 60% what must be the intake temperature for the same exhaust (sink) temperature?
Solution
Efficiency of Carnot engine (η1) = 45% = 0.45
Initial intake temperature (T1) = 327°C = 600 K
New efficiency (η2) = 60% = 0.6
Efficiency of Carnot engine is given by
η = `1 - "T"_2/"T"_1`
T1 is the temperature of the source; T2 is the temperature of the sink
1st Case: T2 = (1 − η)T1 = (1 − 0.45) × 600
T2 = 330 K
2nd Case: `"T"_2/"T"_1 = 1 - η`
T1 = `"T"_2/(1 - η)`
= `330/(1 - 0.6)`
= `330/0.4`
T1 = 825 K
= 825 − 273
T1 = 552°C
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