Two moles of a perfect gas undergo the following processes:
a. A reversible isobaric expansion from `(1.0 atm, 20.0L)` to `(1.0 atm, 40.0L)`
b. A reversible isochroic change of state from `(1.0 atm, 40.0L)` to `(0.5 atm, 40.0 L)`
c. A reversible isothermal expansion from `(0.5 atm, 40.0 L) to(1.0 atm, 20.0 L)`
i. Sketch with lables 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 process.
iii. What will be the values of `DeltaH` for the overall process?

Explanation

a.
b. Total work done `(w) = w_(1) +w_(2) +w_(3)`
`=- P DeltaV +0 +2.303 nRT log.(V_(1))/(V_(2))`
`=- 1 xx 20 +@.303 xx2xx 0.082 x121.95 log.(40.0)/(20.0)`
(Here `T = (PV)/(nR) =(1xx20)/(2xx0.082) = 121.95K)`
`=- 20 +13.86 =- 6.14 L-atm`
Since the system has returned to its initial state i.e., the process is cyclic, `DeltaU = 0`
But `DeltaU = q +w`
`:.q =- w = 6.14 L-atm = 6.14 xx 101.3 J = 621.0 J`
c. `DeltaH,DeltaH`, are state functions, and the system has returned to the original state.
`DeltaH = 0, DeltaH = 0`