A constant amount of an ideal gas undergoes cyclic process A B C A in p-V graph shown below. path B

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11.Thermodynamics

hard

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 .......... $\,kJ$

A

$600$

B

$300$

C

$-300$

D

$-600$

(KVPY-2011)

Solution

(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

$W_{C A B C}=W_{C A}+W_{A B}+W_{B C}$

$=0+p \Delta V+\int p d V$

$=200(5-2)+\int \limits_5^2 k \frac{d V}{V}$

$=600+k \int \limits_5^2 \frac{d V}{V}$

$=600+1000(\log 2-\log 5)$

$=600+1000(0.69-160)$

$=600-910 \approx-300 \,kJ$

Standard 11

Physics

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