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 isochoric change of state from (1.0 atm, 40.0 L) to (0.5 atm, 40.0 L)
(c ) a reversible isothermal compression from (0.5 atm, 40.0 L) to (1.0 atm, 20.0 L)
(i) Sketch the labels of each of the processes on the same p-V diagram.
(ii) Calculate the total work (W) and the total heat change (q) involved in the above processes.
(iii) What will be the values of `DeltaU, DeltaH` and `DeltaS` for the overall process ?

Explanation

(i) State A : (`1.0` atm `20L`)
State B : (`1.0` atm , `40L`)
State C : (`0.5` atm, 40 L)

`(ii) (a)` State A to State B (Isobaric expansion)
Work done by the gas `=W_(1)=-p(V_(B)-V_(A))`
`=-(40-20)=-20L`.atm
(b) State B to State C (Isochoric process)
Work done by the gas `=W_(2)=0` `( :. DeltaV=0)`
(c ) State C to State A (Isothermal compression)
Work done on the gas `=W_(3)=-2.303nRTlog.(V_(A))/(V_(C ))`
`=-2.303pVlog.(V_(A))/(V_(C ))`
`(pV=p_(A)V_(A)=p_(B)V_(B)=nRT=20)`
`=-2.303xx20log.(20)/(40)=+13.864 L`. atm
`:.` total work done by the gas
`=W_(1)+W_(2)+W_(3)=-20+0+13.864=-6.136L`. atm
`=-(6.136xx8.314)/(0.0821)J`
`=-621.37J`
And, `q=-W=621.37J` (` :.` in cyclic process, `DeltalI=0`)
(iii) The total process is cyclic and LI, H and S are state functions
`:. DeltalI=0`, `DeltaH=0` and `DeltaS=0`