# Ideal Gas Law with Compressibility Factor

on . Posted in Thermodynamics

The ideal gas law with compressibility factor is used for higher pressure and temperature than the ideal gas law that is at atmospheric conditions.

## Ideal Gas Law with Compressibility Factor formula

$$\large{ p \; V = z \; n \; R \; T }$$     (Ideal Gas Law with Compressibility Factor)

$$\large{ p = \frac{ z \; n \; R \; T }{ V } }$$

$$\large{ V = \frac{ z \; n \; R \; T }{ p } }$$

$$\large{ z = \frac{ p \; V }{ n \; R \; T } }$$

$$\large{ n = \frac{ p \; V }{ z \; R \; T } }$$

$$\large{ R = \frac{ p \; V }{ z \; n \; T } }$$

$$\large{ T = \frac{ p \; V }{ z \; n \; R } }$$

Symbol English Metric
$$\large{ p }$$ = pressure of gas  $$\large{\frac{lbf}{in^2}}$$  $$\large{Pa}$$
$$\large{ V }$$ = volume of gas $$\large{ in^3 }$$ $$\large{ mm^3 }$$
$$\large{ z }$$ = compressibility factor (1.0 is the ideal gas) $$\large{dimensionless}$$
$$\large{ n }$$ = number of moles of gas $$\large{dimensionless}$$
$$\large{ R }$$ = specific gas constant (gas constant) $$\large{\frac{ft-lbf}{lbm-R}}$$  $$\large{\frac{J}{kg-K}}$$
$$\large{ T }$$ = temperature of gas $$\large{ F }$$ $$\large{ K }$$ 