A diatomic ideal gas is used in Carnot's engine as working substance. During adiabatic expansion of the…

A diatomic ideal gas is used in Carnot's engine as working substance. During adiabatic expansion of the cycle, if the volume of the gas increases from $V$ to $32 \mathrm{~V}$, then the efficiency of the engine is
  1. 0.25
  2. 0.5
  3. 0.67
  4. 0.75

Solution


Given, volume at $C=V$ and volume at $D=32 \mathrm{~V}$ For adiabatic expansion $C D$, $ \begin{aligned} T_C V_C^{\gamma-1} & =T_D V_D^{\gamma-1} \Rightarrow \frac{T_C}{T_D}=\left(\frac{V_D}{V_C}\right)^{\gamma-1} \\ & =\left(\frac{32 V}{V}\right)^{\gamma-1}=32^{\frac{7}{5}-1} \\ \Rightarrow \quad \frac{T_C}{T_D} & =(32)^{\frac{2}{5}}=4 \end{aligned} $ Now, efficiency of Carnot's cycle, $ \eta=1-\frac{T_D}{T_C}=1-\frac{1}{4}=\frac{3}{4}=0 \cdot 75 $

Asked in: AP EAMCET 2018 (22 Apr Shift 2)

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