One mole of a gas is carried through the cycle shown in Fig. The gas expands at constant temperature `T` from volume `V` to `2V`. It is them compressed to the initial volume at constant pressure and is finally brought back to its original state by heating at constant volume. Calculate the work done by the gas in complete cycle.

Explanation

Work done in isothermal process `A` to `B`
`W_(AB) = nRT 1n (V_(f))/(V_(i)) = RT 1n (2V)/(V) [ :' n = 1]`
If pressure at `B` is `P_(B)`, then
`P_(A) V_(A) = P_(B) V_(B)`
or `PV = P_(B) xx 2 V implies P_(B) = P//2`
Work done in isobaric process from `B` to `C` at constant pressure `P//2`
`W_(BC) = P_(B) (V_(f) - V_(i))`
`= (P)/(2) (V - 2V) = - (PV)/(2)`
`= (-RT)/(2)`
Work done in isochoric process `C` to `A`, `W_(CA) = 0`
Therefore work done in the whole cycle,
`W = W_(AB) + W_(BC) + W_(CA)`
`= RT 1n 2 - (RT)/(2) + 0`
`RT (1n 2 - (1)/(2))`