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Question

Two Carnot engines A and B are operated in series. The first one A receives heat from a source at temperature 800 K and rejects heat to a reservoir at temperature T K. The second engine B receives the heat rejected by the first engine and in turn rejects to a heat reservoir at temperature 300 K Find the value of temperature T if the efficiencies of two engines are equal.
(Take 6=2.45 for calculation)

A
550 K
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B
300 K
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C
25×104 K
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D
490 K
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Solution

The correct option is D 490 K
For engine A,
Temperature of source T1=800 K
Temperature of sink T2=T K
For engine B, sink of engine A is acting as a source reservoir. Hence for engine B,
Temperature of source, T1=T K
Temperature of sink, T2=300 K

Since, the efficiencies of two engines are equal.
ηA=ηB
1T2T1=1T2T1
T2T1=T2T1
T800=300T
T2=24×104
T=100×24=26×100
substituting 6=2.45,
T=4.90×100=490 K

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