Please show work The work, W, associated with changing the volume of a piston-cy
ID: 1812789 • Letter: P
Question
Please show work
The work, W, associated with changing the volume of a piston-cylinder assembly from an initial volume of Vi to a final volume of Vf can be determined by evaluating the integral W = - PE dV where PE is the external pressure. Compare the work (in J) for the compression of 5.00 mol of an ideal gas: held at a constant temperature of 500. K, from an initial volume of 1.00 times 10-2 m3 to a final volume of 4.00 times 10-3 m3, among the following situations: The compression occurs against a constant external pressure of 1.00 times 107 Pa; The compression occurs against an external pressure that varies with the cylinder's volume as PE = nRT/V The compression occurs against an external pressure that varies with the cylinder's volume as PE = Pi /V3/2 where Pi = 2.08 times 106 Pa.Explanation / Answer
n = 5 , T = 500 K Vf = 4 x 10^-3/m^3 , Vi = 1 x 10^-2/m^3 On integration at each case we get, (a.) W = - Pe x (Vf - Vi) = 60 kJ (b.) W = n R T ln(Vf) -n R T ln(Vi) = 5 x 8.314 x 500 x ln(10/4) = 19.045 kJ (c.) W = Pi x Vi^(3/2) x (-2 x( Vf^(-1/2)-(Vi^(-1/2)) = -65359 kJ