Thermodynamics - Result Question 40
42. Two Carnot engines $A$ and $B$ are operated in series. The engine $A$ receives heat from the source at temperature $T_1$ 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 $T_2$. For what value of $T$ the efficiencies of the two engines are equal?
[NEET Kar. 2013]
(a) $\frac{T_1+T_2}{2}$
(b) $\frac{T_1-T_2}{2}$
(c) $T_1 T_2$
(d) $\sqrt{T_1 T_2}$
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Answer:
Correct Answer: 42. (d)
Solution:
(d) Efficiency of engine $A, \quad \eta_1=1-\frac{T}{T_1}$,
Efficiency of engine $B, \eta_2=1-\frac{T_2}{T}$
Here, $\eta_1=\eta_2$
$\therefore \frac{T}{T_1}=\frac{T_2}{T} \Rightarrow T=\sqrt{T_1 T_2}$
