Question

Two moles of helium gas undergo a reversible cyclic process as shown in figure. Assuming gas to be ideal, what is the net work involved in the cyclic process?

• A. -100 Rln4
• B. +100 Rln4
• C. +200 Rln4
• D. -200 Rln4

Answer 1

Answer: (A)

$W_{\text{net }}=$ area enclosed

$V=\frac{nRT}{P}$

$V_A=\frac{2R\times 300}{1}=\frac{600R}{1}$

$V_B=\frac{2R\times 300}{2}=\frac{300R}{1};$

$V_c=\frac{2R\times 400}{2}=\frac{400R}{1}$

$V_D=\frac{800R}{1}$



$W_{AB}=-nRT{T}_A\ln \frac{V_B}{V_A}=-2R(300)\ln \frac{1}{2}=600Rin2$

$W_{BC}=-2(400-300)R=-200R$

$W_{CD}=-2R(400)\ln \frac{V_D}{V_C}=-800Rin2$

$W_{AD}=-1(600R-800R)=200R$

$W_{\text{Total }}=W_{AB}+W_{BC}+W_{CD}+W_{AD}=200Rin2=-100Rln4$