Question

Two Carnot engines A and B are operated in series. The
engine A receives heat from the source at temperature T₁
and rejects the heat to the sink at temperature T. The second
engine B receives the heat at temperature T and rejects to
its sink at temperature T₂. For what value of T the
efficiencies of the two engines are equal? [NEET Kar. 2013]
(a) T₁ + T₂/2
(b) T₁ - T₂/2
(c) T₁T₂ (d) √T₁T₂

Answer 1

Answer:

Given:

T1=800K

T3=400K

To find:

Temperature T 

(i) when output of two engines are equal

(ii) when efficiencies of two engines are equal.

Let the output of both engines be W.

Let the engine A take Q1 heat as input at temperature T1 and gives out heat Q2 at temperature T the second engine B receive Q2 as input and give out Q3 at temperature T2 to the sink.

Work done by engine, A W=Q1–Q2

Work done by engine, B W=Q2–Q3

Thus,

 Q1–Q2=Q2–Q3

Dividing both sides by Q1,

1–Q1Q2=Q1Q2–Q1Q3

⟹1−T1T=

Answer 2

The answer is (a) T₁ + T₂/2

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