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Question

Two Carnot engines are working between 400K and 300K,300K and 200K respectively. Find the ratio of the efficiency of first system to the second system.

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Solution

System 1:
Temperature of source, T1=400K
Temperature of sink, T2=300K
efficiency of engine is,
η1=1T2T1=1300400=0.25
System 2:
Temperature of source, T1=300K
Temperature of sink, T2=200K
efficiency of this engine is,
η2=1T2T1=1200300=0.33
Ratio of efficiencies is,
η1η2=0.250.33=1/41/3=34=0.75

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