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

$V=\frac{n R T}{P}$

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

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

$ V_{c}=\frac{2 R \times 400}{2}=\frac{400 R}{1}$

$V_{D}=\frac{800 R}{1}$



$W _{ AB }=- nRT \,T _{ A } \ln \frac{V_{B}}{V_{A}}=-2 R (300) \ln \frac{1}{2}=600\, Rin 2$

$W _{ BC }=-2(400-300) R =-200 \,R$

$W _{ CD }=-2 R (400) \ln \frac{V_{D}}{V_{C}}=-800\, Rin\, 2$

$W _{ AD }=-1(600\, R -800 \,R )=200\, R$

$W _{\text {Total }}= W _{ AB }+ W _{ BC }+ W _{ CD }+ W _{ AD }=200 Rin 2=-100 \,Rln \,4$