A constant amount of an ideal gas undergoes the cyclic process $A B C A$ in the $p-V$ graph shown below. The path $B C$ is an isothermal. The work done by the gas during one complete cycle, beginning and ending at $A$ is nearly .......... $\,kJ$
KVPY 2011, Diffcult
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(c)
$\ln$ isothermal process $B C$,
$p V=\text { constant }$
$\Rightarrow \quad D_C V_C=p_B V_B$
$\Rightarrow \quad \frac{p_C V_C-500 \times 2}{p_B}=5\, m ^3$
Now, work done in the complete cycle $C A B C$ is
$W_{C A B C}=W_{C A}+W_{A B}+W_{B C}$
$=0+p \Delta V+\int p d V$
$=200(5-2)+\int \limits_5^2 k \frac{d V}{V}$
$=600+k \int \limits_5^2 \frac{d V}{V}$
$=600+1000(\log 2-\log 5)$
$=600+1000(0.69-160)$
$=600-910 \approx-300 \,kJ$
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