5 kg of gas is contained within a piston-cylinder assembly having an initial tem

Question

5 kg of gas is contained within a piston-cylinder assembly having an initial temperature of 25 degrees Celcius and at an initial pressure of 195 kPa. The gas is compressed to a final pressure of 200 kPa and the piston is displaced a distance of 0.5 m during the compression process. The cross-sectional area of the piston is 0.095 m^2. The universal gas constant is 8.314 kJ/kmol-K and the molecular weight of the gas is 28.97 kg/kmol. The compression process follows the polytropic relation PV^n=constant. Treating the gas as ideal,

Determine a) the initial volume of the gas b)final temperature of the gas c) the value of the exponent n

Explanation / Answer

a) initial volume from, PV=nRT P=195 x 10^3 N/m^2 ; T = 25C = 298K ; R=8.314 kJ/kmol-K ; n=mass/M.W = 5/28.97 = 0.172 kmol => V = nRT/P = 0.172 x 8.314 x 10^3 x 298 / (195 x 10^3) = 2.18 m^3 final volume = initial volume - A x d = 2.18 - 0.095 x 0.5 = 2.13 m^3 (A = cross-sectional area of the piston d = piston displacement) final pressure = 200 x 10^3 N/m^2 PV=nRT => T = PV/nR = 200 x 10^3 x 2.13 / (0.172 x 8.314 x 10^3) = 297.9 K b) P1V1^n = P2V2^n TAKING LOG OF BOTH SIDES logP1 + nlogV1 = logP2 + nlogV2 => n = (logP2 - logP1)/(logV1 - logV2) = 1.09

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