Gas contained in a frictionless piston-cylinder device is initially at a volume

ID: 2995100 • Letter: G

Question

Gas contained in a frictionless piston-cylinder device is initially at a volume of 2 m3 and

pressure of 0.2 MPa (state 1). The gas is then compressed to a final pressure of 0.6 MPa (state 2).

During this particular process, the pressure of the gas inside the piston-cylinder device is found

to vary with the gas volume according to the equation: PV 2 ? C,

where C is a constant. Determine the magnitude (in kJ) and direction of the work involved in the

process.

The answer is suppose to be:

Answer: -293 kJ.

Given

P1 = 0.2 MPa

V1 = 2 m^3

P2 = 0.6 MPa

PV^2 = C

Therfore

P1*V1^2 = P2*V2^2

V2 = 2*(0.2/0.6)^1/2

V2 = 1.155 m^3

Work done in a Polytropic process (PV^n = C) is given by

W = (P1*V1 - P2*V2)/(1-n) = (0.2*2-0.6*1.155)*10^3/(1-2)

W = -293 kJ

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