Sonntag, Borgnakke and van Wylen
8.112 A piston/cylinder contains air at 300 K, 100 kPa. It is now compressed in a reversible adiabatic process to a volume 7 times as small. Use constant heat capacity and find the final pressure and temperature, the specific work and specific heat transfer for the process. Solution: Expansion ratio:
v2/ v1 = 1/7
Process eq.: Rev. adiabatic and ideal gas gives P2 /P1 = (v2/v1)-k = 71.4 = 15.245
Pvn = C, with n = k
P2 = P1 (71.4) = 100 × 15.245 = 1524.5 kPa T2 = T1 (v1/v2)k-1 = 300 × 70.4 = 653.4 K 1q2 = 0 kJ/kg Polytropic process work term from Eq.8.38 R 0.287 1w2 = 1 - k (T2 –T1) = -0.4 (653.4 – 300) = -253.6 kJ/kg Notice: Cv = R/(k-1) so the work term is also the change in u consistent with the energy equation.