A piston-cylinder device initially contains 0.22 kg of steam at 200 kPa and 300°C. Now, the steam is cooled at constant pressure until it is at 150°C. Determine the volume change of the cylinder during this process using the compressibility factor, and compare the result to the actual value.

Defining compressibility factor (Z), which is also known as the gas deviation factor, is a correction factor which describes the deviation of a real gas from ideal gas behaviour.

Z = p / (density * Rs * T)

Where Rs is specific gas constant = R/M

Deriving the volume values from steam tables,

At 200kPa and 300°C, V1 = 1.31623 m3/kg

At 200kPa and 150°C, V2 = 0.95986 m3/kg

Change in volume, DV = m (V1 - V2)

= 0.2 * (1.31623 - 0.95986)

= 0.07128 m3/kg

Also from steam tables,

The critical pressure, Pc = 22.06MPa

The critical temperature, Tc = 647.1K

Remember, gas constant, R = 0.4615 kPa. m3/kg. K

Therefore, reduced temperature at initial state, Tr = T1/Tc

= (360 + 273) / 647.1

= 0.886

Also, reduced pressure at initial state, Pr = P1/Pr

= 200 x 10^-3/22.06

= 0.0091

But compressibility factor at initial state, Z1 = 0.9956

Ideal volume, Vi = m*R*T/P1

= (0.2*0.4615 * (300+273)) / 200

= 0.2644m3

Compressibility volume, Vc = Z1*Vi

= 0.9956 * 0.2644

= 0.2633m3

Reduced temperature at final state, Tr = T2/Tc

= (150+273) / 647.1

= 0.65

Reduced pressure at final state, Pr = P2/Pc

= 200 x 10^-3/22.06

= 0.0091

Compressibility factor at final state, Z2 = 0.9897