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Question

An ideal Carnot engine having efficiency η works between temperatures 127°C and 73°C. η1 denotes the efficiency when the temperature of the source increases by 50°C and η2 denotes efficiency when temperature of the sink decreases by 50°C. Then the correct order is

A
η>η1>η2
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B
η1>η>η2
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C
η2>η1>η
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D
η=η1=η2
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Solution

The correct option is C η2>η1>η

T1=127o=400 KT2=73o=200 K
effeciency (η)=1T2T1
η=1200400 =112
=50%

Case 1: T1=450 KT2=200 K
η1=1T2T1 =1200450
=55%

Case 2: T1=400 KT2=150 K
η2=1T2T1 =1150400
=62.5%

From above observation, η2>η1>η

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