Q. A 1 gm nitrogen undergoes a following sequence of process in a piston cylinder arrangement.(1) An adiabatic expansion in which volume double. (2) A constant pressure process in which volume is reduced to its initial state. Represent the cycle on p -v diagram, calculate net work done by the gas.

 Q. A 1 gm nitrogen undergoes a following sequence of process in a piston cylinder arrangement.(1) An adiabatic expansion in which volume double. (2) A constant pressure process in which volume is reduced to its initial state. Represent the cycle on p -v diagram, calculate net work done by the gas.

Assuming  t1 = 150°C , P1 = 5 atm, Y = 1.4, R = 297 J/kg K.

Solution: t1 = 150°C

                  T1 = 150 + 273 = 423 K

                  P1 = 5 × 1.01325 = 5.06625 bar

Process (1-2):

T2/T1 = (V1/V2)^Y-1

T2/423 = (V1/2V1)^1.4-1

T2 = 320.5K

Process(2-3):

T3/T2 = V1/V2

T3/T2 = V1/2V1

T3 = T2/2

T3=320.5/2=160.25K

Now :

W(net) = W(1-2) + W(2-3) + W(3-1)

W(net) = P1V1 -P2V2/Y-1  + P3V3 -P2V2 + 0

W(net) = mR(T1-T2)/Y-1   + mR(T3-T2)

W(net) = 10^-3 × 297(423 - T2)/1.4 -1  + 10^-3×297(T3 - T2)

W(net) = 10^-3 × 297(423 - 320.5)/0.4 + 10^-3×297(160.25 - 320.5)

W(net) = 28.86 J