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Question

Two Carnot engines A and B are operated in series. The first engine, A, receives heat at 800 Kand rejects to a reservoir at temperature T. The second engine B receives the heat rejected by the first engine and in turn rejects to a heat reservoir at 300 K. Find the value of T, when the work outputs of the engines are equal.

A
0 K
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B
1100 K
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C
550 K
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D
300 K
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Solution

The correct option is C 550 K

Work done by engine A,

WA=Q1Q2

Work done by engine B,

WB=Q2Q3

As given, WA=WB

Q1Q2=Q2Q3

Dividing on both side by Q1,

1Q2Q1=Q2Q1Q3Q1

1Q2Q1=Q2Q1(1Q3Q2)

1TT1=TT1(1T3T)

T1T1=1T3T

T1T+T3T=2

​​​​​​​T1+T3T=2

​​​​​​​T=T1+T32=800+3002

T=550 K

​​​​​​​​​​​​​​Hence, option (C) is the correct answer.

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