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Air goes through a polytropic process from 325 K, 125 kPa to 500 K, 300 kPa. Find the specific work in the process.

Air goes through a polytropic process from 325 K, 125 kPa to 500 K, 300 kPa. Find the specific work in the process. Correct Answer -51.8 kJ/kg

Process: Pv^(n) = Const = P1(v1)^n = P2(v2)^n Ideal gas Pv = RT hence v1 = RT/P = 0.287 × 325/125 = 0.7462 m^3/kg v1 = RT/P = 0.287 × 500/300 = 0.47833 m^3/kg n = ln(P2/P1) / ln(v1/v2) = ln 2.4 / ln 1.56 = 1.969 Work = (P2v2 – P1v1)/(1-n) = R(T2-T1)/(1-n) = 0.287(500 – 325)/(1-1.969) = -51.8 kJ/kg.

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