Find the compressibility factor of a superheated H2O vapor a

Find the compressibility factor of a superheated H_2O vapor at 150 bar and 500 degree C using the following two methods: (a) the definition of compressibility: Z = pv/RT; and (b) the Nelson-Obert chart in Figure A-15. Please justify if H_2O under given conditions can be considered as ideal gas based on the compressibility factor calculated. The critical pressure, critical temperature, and gas constant R of water can be found in Table A-l. Please find the specific volume of a pure O_2 at 200 K and 2.0 MPa by the two methods: Employ the ideal gas equation. Use the compressibility chart if the critical point for O_2 is known: T_cr = 154.6K, p_cr = 5.05 MPa.

Solution

6.a) From steam table A-6 superheated vapour Yunus Cengel and Boles

at T= 500^oC and P= 150 bar

v = 0.020828 m³/kg

Z = (Pv) / (RT) = (150 X 10⁵ X0.020828) / ((8.314 / 18.02) X 773) = 0.875

Hence compressibility factor Z = 0.875

6.b) From Table A-1 Yunus Cengel and Boles

Crital Pressure (P_c) of Water = 220.6 bar

Critical Temperature of Water (T_c) = 647.1 K

Hence,

Reduced Pressure (P_r) = P/P_c = 150 / 220.6 = 0.679

Reduced Temperature (T_r) = T/T_c = (500+273) / 647.1 = 1.19

Hence from Nelson - Obert generalized compressibility chart

Z = 0.86