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Question

For a Carnot engine T1>T2 . When T2 is decreased by ΔT with T1 remaining same then efficiency is η1 and when T1 is increased by ΔT with T2 remaining same , efficiency is η2 which one of the following is the correct expression for η1 ,η2?

A
(T2+T1)ΔT+(ΔT)2T1(T1+ΔT)
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B
(T2T1)ΔT+(ΔT)2T1(T1+ΔT)
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C
η1=1(T2ΔT)T1
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D
η2=1(T2)T1+ΔT)
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Solution

The correct option is A (T2+T1)ΔT+(ΔT)2T1(T1+ΔT)
η1η2=T2T1+ΔTT2ΔTT1

=T1T2(T1+ΔT)(T2ΔT)T1(T1+ΔT)

=T1T2[T1T2+T2ΔTT1ΔT(ΔT)2]T1(T1+ΔT)

=(T1T2)ΔT+(ΔT)2T1(T1+ΔT)

=(T2T1)ΔT+(ΔT)2T2(T2+ΔT)

=(T1+T2)ΔT+(ΔT)2T2(T1+ΔT)

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