Answer to Question #230593 in Mechanical Engineering for Thoh

Question

Determine the specific volume of superheated water vapour 3.5 MPa and 460 C using: a) The ideal-gas equation b) c) The generalized compressibility chart and The steam tables

Answer 1

Given

Pressure, P = 3.5 MPa

Temperature, T = 450 ^oC = 723 K

step: 2 of 5

a) Assuming, the superheated water behaves as an ideal gas at specified conditions.

For water, gas constant R = 0.4615 kJ/kg K (from Table-1)

From the ideal gas equation, specific volume is given by

 $V=\dfrac{RT}{P}$

= 0.095 m³/Kg

.

step: 3 of 5

b) The critical pressure and temperature of water are

P_cr = 22.06 MPa

T_cr = 647.1 K

Therefore,

Reduced pressure,

P_r = 0.158

Reduced temperature,

T_r = 1.12

From compressibility chart (A-15), corresponding to the obtained P_r and T_r values, we have

Z = 0.96

Therefore, actual specific volume is

v_actual = 0.09152 m³/kg

step: 4 of 5

c) For superheated water (from Table A-6)

For pressure, P =3.5 MPa

and T = 450 ^oC

We have,  0.09152 m^3/Kg

step: 5 of 5

The error involved in the first case is,

Error = 3.64%

The error involved in the second case is,

Error = 0.5 %