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

(i)
(ii) Total work (W) = `W_(A rarr B) + W_(B rarr C) + W_(C rarr A)`
`W_(A rarr B) = -P(V_(B)-V_(A)) = -1(40 - 20) = - 20` atm.L
`W_(B rarr C)` = isochoric change `Delta V = 0`
`W_(C rarr A)` (isothermal compression)
`=-"2.303 nRT log"((V_(A))/(V_(C)))" "(PV = nRT)`
`=-2.303 xx 0.5 xx "40 log"(20)/(40)`
= + 13.864 atm.L
Total work done = (-20 + 13.864) atm.L
= -6.136 atm.L
Since the process is cyclic, `Delta E - 0` (because E is state function)
`Delta Q = Delta E - Delta W`
`Delta Q = - Delta W` = + 6.136 atm.L
(iii) `Delta E, Delta H, Delta S` will be zero for overall process because E, H and S are state functions.