Question

I'm having trouble finding the thermodynamic temperature of Oxygen at a pressure 10000 kPa and 0.005 m3 /kg using virial equation of state. I have found that Oxygen Critical Temperature is 155.15 K and Oxygen Critical Pressure is 50 atm; M = 32 g/mol. The second virial coefficient is B (cm³ /mole), and I am given the following data.

T(K)	B(cm3/mol)
100	-200
273	-22
373	-4
600	13

Answer 1

Here best way is to Find B as a function of temperature first with the help of data provided. To this we will plot the data and find the equation using curve plotting method

T(K)	B(cm3/mol)
100	-200
273	-22
373	-4
600	13

From above equation

B = -0.0015 *T² + 1.4786*T - 328.69

now ,we will given volume in terms of molar volume

V = 0.005 m³/Kg =5 cm³/g * 32 g/mol= 160 cm³/mol

Viral equation is given by

Now here we have all data except "T", Hence we will substitute rest of the known data and find the value of T

R = 8.314 cm³ MPa/mol K

P = 10000 KPa = 10 MPa

v =160 cm3/mol

T =263.5732 K