Explanation:
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
