a cylinder fitted with a frictionless piston contains 500L of air at 110 kPa, 25

Question

a cylinder fitted with a frictionless piston contains 500L of air at 110 kPa, 25 C. The air is compressed in a reversible polytropic process to a final pressure of 800 kPA, at which point the temperature is 140 C. Assuming that heat transfer is with the ambient at 25 C determine: The polytropic N the final volume the work done on the air and heat transfer for the process the net change in entropy for the process. I attempted this problem and got n=1.196 however my work was 168 which is incorrect. any suggestion?

Explanation / Answer

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Inputs:

V1 = 500 [L] = 0.5[m3]

P1 = 110 [kPa]

T1 = 25 [C] = 298 [K]

MW = 28.97 [g/mol]

T2 = 140 [C] = 413 [K]

P2 = 800 [kPa]

Solutions:

Polytropic Index:

n = ln(T1/T2) - ln(P1/P2)
n = -1 / [ (ln(298 [K] / 413 [K]) - ln(110 [kPa] / 800 [kPa])) - 1]
n = 1.197

Work:
W = R(T2 - T1) / (1-n)
W = 0.28699 [J/g-K](413 [K] - 298 [K]) / (1 - 1.197)
W = -167.53223 [J]

Volume 2:
V2 = V1*[(T1/T2)1/(n-1)]
V2 = 0.5 [m3] * [(298 [K] / 413 [K])1/(1.197-1)]
V2 = 0.095 [m3]

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