A rigid tank contains 05 kg of oxygen initially at 30 bar an

A rigid tank contains 0.5 kg of oxygen initially at 30 bar and 200 K. The gas is cooled and the pressure drops to 20 bar. Determine the volume of the tank and the final temperature (use the generalized compressibility chart).

Solution

Given, for oxygen, m =0.5 kg

P1 = 30 bar = 30 x 10^5 Pa

T1 = 200 KP2 =20 bar

Volume of the tank = ? for oxygen R = R\'/M = 8.314/ 31.988 =0.259832 kJ/kg K = 259.832 J/kg K

from compressibility chart Z = 0.90733 (FOR OXYGEN)

Using gas equation: PV = Z x mRT

V = ZmRT/P = 0.90733 x 0.5 x 259.832 x 200 / 30 x 10^5 = 0.00788 m^3

NOW T2 =? (Z = 0.819) at P2 and V (V is constant as tank is rigid)

PV =ZmRT or T2= PV/ZmR = 20 x 10^5 x 0.00788 / 0.819 x 0.5 x259.832 = 148.118 K