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

419 Points
10 years ago

Dear Student

$Z=\frac{p \tilde{V}}{R T}$

where, p is the pressure, $\tilde{V}$ 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:

$T_r = \frac{T}{T_c}$ and $P_r = \frac{P}{P_c}$

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.

$T_r = \frac{T}{T_c + 8}$ and $P_r = \frac{P}{P_c + 8}$

now you can eliminate T and P and put in terms of critical temp and pressure.

All the best.

AKASH GOYAL

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509 Points
10 years ago

Pc = a/27b2 , Tc = 8a/27Rb , Vc = 3b

a,b are vanderwalls equation constants

Z = PV/RT = 3/8