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Helium in a piston/cylinder at 20°C, 100 kPa is brought to 400 K in a reversible polytropic process with exponent n = 1.25. Helium can be assumed to be an ideal gas with constant specific heat. Find the specific work.

Helium in a piston/cylinder at 20°C, 100 kPa is brought to 400 K in a reversible polytropic process with exponent n = 1.25. Helium can be assumed to be an ideal gas with constant specific heat. Find the specific work. Correct Answer -887.7 kJ/kg

Process: Pv^(n) = C & Pv = RT => Tv^(n-1) = C Cv = 3.116 kJ/kg K, R = 2.0771 kJ/kg K v2 / v1 = (T1 / T2 )^ = 0.2885 P2 / P1 = (v1 / v2)^(n) = 4.73 => P2 = 473 kPa W = (P2 v2 – P1 v1)/(1-n) = R(T2-T1)/(1-n) = -887.7 kJ/kg.

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