Sonntag, Borgnakke and van Wylen
4.51 Air goes through a polytropic process from 125 kPa, 325 K to 300 kPa and 500 K. Find the polytropic exponent n and the specific work in the process. Solution: n
n
Process:
Pvn = Const = P1v1 = P2 v2
Ideal gas
Pv = RT
so RT 0.287 Ă— 325 = 0.7462 m3/kg v1 = P = 125
RT 0.287 Ă— 500 v2 = P = = 0.47833 m3/kg 300 From the process equation (P2/ P1) = (v1/ v2)
n
=> ln(P2/ P1) = n ln(v1/ v2) ln 2.4 n = ln(P2/ P1) / ln(v1/ v2) = ln 1.56 = 1.969 The work is now from Eq.4.4 per unit mass P2v2-P1v1 R(T2 - T1) 0.287(500 - 325) = = = -51.8 kJ/kg 1w2 = 1-n 1-n 1-1.969