Air in a piston-cylinder assembly is slowly compressed from 100kPa to 300kPa. Th

Question

Air in a piston-cylinder assembly is slowly compressed from 100kPa to 300kPa. The mass of the air is 1.5X10-4Kg, and its initial temperature is 20oC. During the entire process, pressure is related to volume as
PV1.4= a constant
Calculate the work done.

Explanation / Answer

Pi = 100 kPa Pf = 300 kPa Ti = 20 deg. C = 293.15 K n = k = 1.4 W = ?PdV, PV^n = C --> P = C/V^k W = ?C/V^k dV W = C?V^-k dV W = PfVf - PiVi / 1-k ........ (1) Solve for Vf and Vi PV = nRT = PiVi = nRTi PiVi = m(R/Mr)Ti Vi = m(R/Mr)Ti / Pi, Mr air = 28.97 Vi = 1.5X10-4*(8.314/28.97)*293.15 / 100 Vi = 0.0001262 m^3 = 126.2 cm^3 PiVi^1.4 PfVf^1.4 Vf = 57.58 cm^3 Solve for (1) W = PfVf - PiVi / 1-k W = 300*57.58*10^-6 - 100*126.2*10^-6 / -0.4 W = - 11635*10^-6 kJ W = - 11.635 J

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