Two moles of a perfect gas undergo the following processes:
(a) a reversible isobaric expansion from (1.0 atm , 20.0 L) to (1.0 atm, 40.0 L)
(b) a reversible isochroic change of state from (1.0 atm , 40.0L) to (0.5 atm , 40.0 L)
(c) a reversible isothermal compression from (0.5 atm,40.0 L ) to (1.0atm, 20.0L)
Calculate the magnitude of work (W) done in L.atm

Answer

(a) -20 L atm (b) `W_(2)=(because) DeltaV=0`) (c) 6 L atm

Explanation

(a) State A to state B (Isobasric expansion)
Work done by the gas =`W_(1) =- p(V_(B) - V_(A)) =- 1(40-20) =- 20L atm`
(b) State B to state C (isochoric process )
Work done by the gas `=W_(2) =0.(because DeltaV=0)`
(c) State C to state A (isothermal compression)
Work done on the gas `= W_(3) =- 2.303 nRT "log" (V_(A))/(V_(C))`
`=-2.303 pV"log"(V_(A))/(V_(C)) (pV=p_(A)V_(A) =p_(B)V_(B)="nRT"=20) =-20ln(1/2)=20 xx ln(2)=14`
`therefore ` total work done by the gas
`=W_(1) + W_(2) + W_(3) =-20 + 0+14 =- 6 L atm`