Two moles of a perfect gas undergo the following process: (a) A reversible isobaric expansion from (`1.0` atm, `20.0` litre) to (`1.0` atm,`40.0`litre). (b) A reversible isochoric change of state from (`1.0` atm, `40.0` litre) to (`1.0` atm, `40.0` litre). (b) A reversible isochoric change of state from (`1.0` atm, `40.0` litre) to (`0.5` atm, `40.0` litre). (c) A reversible isothermal compression from (`0.5`atm, `40.0` litre) to (`1.0` atm, `20.0` litre). (i) Sketch with labels each of the process 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 value of `DeltaU, DeltaH` and `DeltaS` for the overall process?

Explanation

(i)
`AB-` isobaric expansion
`BC-` isochoric change
`CA-` isothermal compression
(ii) Now total work `W=W_(AtoB)+W_(BtoC)+W_(CtoA)`
`:. W=-P(V_(2)-V_(1))+0+2.303nRT"log"(V_(3))/(V_(1))`
`=-1xx(40-20)+0+2.303xxP_(1)V_(1)"log"(V_(3))/(V_(1))`
`( :' P_(1)V_(1)=nRT)`
`=-20+2.303xx1xx20"log"(40)/(20)=-6.13 litre atm`
`=(6.13xx8.314)/0.0821J=-620.77 J`
Also `W=q=-620.77 J` (For cyclic process)
(iii) The overall process is cyclic one i.e., initial state is regained, thus
`DeltaU=0,DeltaH=0` and `DeltaS=0`