Determine net work done:

5m³ of air at 2bar, 27⁰C is compressed to 6bar pressure following PV^1.3  = constant. It is expanded subsequently adiabatically to 2 bar. Considering two processes to be reversible, determine net work done, and also plot the processes on T - S diagrams.                                                                                                                                        

Sol:  V₁ = 5m³, P₁  = P₃ = 2bar, P₂  = 6bar, and n = 1.3

V₂ = V₁(P₁/P₂)1/1.3  = 5(2/6)1/1.3  = 2.147m3

Thus work done during process 1 - 2 is W1-2

= (P₂V₂  - P₁V₁)/(1- n)

= (6 × 105  × 2.47 - 2 x 10⁵  × 5)/(1-1.3) = - 9.618 × 10⁵  J

Likewise to obtain work done during processes 2 - 3, we apply

W_2-3 = (P₃V₃  - P₂V₂)/(1 -   ); where      = 1.4

And V₃ = V₂(P₂/P₃)1/   = 2.147(6/2)^1/1.4  = 4.705m³