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Question

Three Carnot engines operate in series between a heat source at a temperature T1 and a heat sink at temperature T4 (see figure). There are two other reservoirs at temperature T2, and T3, as shown, with T2>T2>T3>T4. The three engines are equally efficient if__?
1331085_55af4ef063b6464f9d376a23e83b3a6f.png

A
T2=(T21T4)1/3:T3=(T1T24)1/3
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B
T2=(T1T24)1/3:T3=(T21T4)1/3
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C
T2=(T31T4)1/4:T3=(T1T34)1/4
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D
T2=(T1T4)1/2:T3=(T21T4)1/3
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Solution

The correct option is C T2=(T21T4)1/3:T3=(T1T24)1/3
Given: t1=1T2T1=1T2T2=1T4T3
T2T1=T3T2=T4T3
T2=T1T3=T1T2T4

T(11/4)2=T1/21T1/44
T3/42=T1/21T1/44

T2=(T21T4)1/3

T3=T2T4=(T21T4)1/3T4=T1/31T2/34.

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