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Question: Answered & Verified by Expert
$N$ moles of a monoatomic gas is carried round the reversible rectangular cycle $A B C D A$ as shown in the diagram. The temperature at $A$ is $T$. The
thermodynamic efficiency of the cycle is

PhysicsThermodynamicsAIIMSAIIMS 2004
Options:
  • A $15 \%$
  • B $50 \%$
  • C $20 \%$
  • D $25 \%$.
Solution:
1842 Upvotes Verified Answer
The correct answer is: $50 \%$
At $A$, temperature $=T_0$, volume $=V_0$, pressure $-P_0$ for $n$ moles of monoatomic gas. At $A, P_0 V_0=n R T_0$ (cold)
At $B, 2 P_0 V_0=n R T_{\text {high }}^{\prime} \Rightarrow T^{\prime}=2 T_0$
Maximum thermal efficiency of the reversible engine of this Carnot's cycle
$$
=\eta=1-\frac{T_C}{T_h}=1-\frac{T_0}{2 T_0}=\frac{1}{2}=50 \% .
$$

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