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One mole of oxygen undergoes a cyclic process in which volume of the gas changes 10 times within the cycle, as shown in the figure.
Process : 1-2 and 3-4 are adiabatic.

2-3 and 4-1 are isochoric.
Find the efficiency of the process.

Option: 1
$40%$

Option: 2
$50%$

Option: 3
$60%$

Option: 4
$70%$

Answers (1)

best_answer

$\mathrm{ W_{12}=\frac{R}{1-\gamma}\left[T_2-T_1\right] }$

Since $\mathrm{ T_2 V_2^{\gamma-1}=T_1 V_1^{\gamma-1} }$

$\mathrm{\therefore \quad T_2=T_l \alpha^{\gamma-1} \quad where \: \: \alpha=\frac{V_1}{V_2}}$

Thus, $\mathrm{W_{I 2}=\frac{R T_2}{1-\gamma}\left[1-\frac{1}{\alpha^{\gamma-1}}\right].}$

Similarly, $\mathrm{T_3=T_4 \alpha^{\gamma-I} and W_{34}= \frac{R T_3}{1-\gamma}\left[\frac{1}{\alpha^{\gamma-1}}-1\right]}$

Also $\mathrm{\quad W_{23}=0, W_{41}=0}$

$\mathrm{\therefore W_{n e t}=W_{l 2}+W_{23}+W_{34}+W_{4 l}=\frac{R\left(T_2-T_3\right)}{1-\gamma}\left[1-\frac{1}{\alpha^{\gamma-1}}\right] }$

$\mathrm{ Q_{\text {in }}=\frac{R}{\gamma-1}\left[T_3-T_2\right]=\frac{R}{1-\gamma}\left[T_2-T_3\right] }$

$\mathrm{ \therefore \eta=\frac{W_{\text {net }}}{Q_{\text {in }}}=1-\frac{1}{\alpha^{\gamma-1}} }$

$\mathrm{\text { Here } \alpha=10 ; \gamma=1.4 }$

$\mathrm{\therefore \quad \eta=60 \%}$

$$

Posted by

Shailly goel

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