how to express compressibility factor in terms of critical pressure and critical volume

							

Dear Student
 

 
where, p is the pressure,  is the molar volume of the gas, T is the temperature, and R is the gas constant.
For an ideal gas the compressibility factor is Z = 1 per definition
The reduced temperature and pressure are defined as:
 and 
Tc and Pc are known as the critical temperature and critical pressure of a gas. They are characteristics of each specific gas with Tc being the temperature above which it is not possible to liquify a given gas and Pc is the minimum pressure required to liquify a given gas at its critical temperature.
 and 
 
now you can eliminate T and P and put in terms of critical temp and pressure.
 
All the best.                                                           
AKASH GOYAL
AskiitiansExpert-IIT Delhi
 
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Pc = a/27b2 , Tc = 8a/27Rb , Vc = 3b
a,b are vanderwalls equation constants
Z = PV/RT = 3/8