Question

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?

Answer 1

`AB to`Isobaric process
BC`to` Isochoric process
`CA to` Isothermal compression

Total work `=w_(AB)+w_(BC)+w_(CA)` ltbr. `=-PxxDeltaV+0+2.303nRT" log "((V_(2))/(V_(1)))`
`=-1xx20xx101.3+0+2.303xx2xx8.314xxT" log "((40)/(20))` . . .(i)
`PV=nRT` (At A)
`1xx20=2xx0.082xxT`
`T=(20)/(2xx0.0821)=121.8K`
From eq. (i)
Total work=`-2026+2.303xx2xx8.314xx121.8" log "2`
`=-622.06J`
`w=q=-622.06J`
In cyclic process, `DeltaU=0,DeltaH=0 and DeltaS=0`.