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 ?

Options

A. `-100 Rl n4`
B. `+100 Rl n4`
C. `+200 Rl n4`
D. `-200 Rl n 4`

Answer

A

Explanation

`W_("total")= "area enclosed"`
`V=(RT)/(P)`
`V_(A)=(2Rxx300)/(1)=(600R)/(1)`
`V_(B)=(2Rxx300)/(2)=(300R)/(1), V_(c )=(2Rxx400)/(2)=(400R)/(1)`
`V_(D)=(800R)/(1)`
`W_(AB)= - nRT_(A)" ln"(V_(B))/(V_(A))=-2R(300)"ln"(1)/(2)=600 Rln2`
`W_(BC)= -2(400-300)R= -200R`
`W_(CD)= -2R(400)"ln"(V_(D))/(V_(c ))= -800 R sin 2 rArr W_(AD)= -1(600R-800R)=200R`
`W_("Total")=W_(AB)+W_(BC)+W_(CD)+W_(AD)= -200 R sin 2= -100 R ln4`