A pistoncylinder device contains 0150 kg of air initially at

A piston-cylinder device contains 0.150 kg of air initially at 1.9 MPa and 348 degree C. The air is first expanded isothermally to 420 kPa, then compressed polytropically with a polytropic exponent of 1.227 to the initial pressure, and finally compressed at the constant pressure to the initial state. Determine the boundary work for each process and the net work of the cycle. Round all answers to two decimal places W1-2 = kJ W2-3 = kJ W3-1 = kJ Wnet = kJ

Solution

If air properties are calculated at 348 K, then from Table we get,

R = 0.287 kJ/kg K

k = 1.4

V1 = mRT/P1 = 0.15 * 0.287 * (348+273.15)/1900 = 0.0202 m^3

V2 = mRT/P2 = 0.15 * 0.287 * (348+273.15)/420 = 0.0636 m^3

The work for an isothermal process:

W12 = P1V1 ln(V2/V1) = 1900 * 0.0202 ln(0.0636/0.0202) = 44.01 KJ

For polytropic compression P V^n = constant

P2V2^n=P3V3^n

420*0.0636^1.227 = 1900*V3^1.277

14.291/1900 = V3^1.277

V3 = 0.0195 m^3

W23=(P3V3 - P2V2)/(1-n)

= (1900 *0.0195 - 420*0.0636)(1-1.277)

= - 37.32 KJ

W31=P3(V1- V3)

= 1900(0.0202 - 0.0195) =37.65 KJ

Wnet = W12+W23+W31 = 44.01 - 37.32 +37.65 = 44.34 KJ