Question

Compressibility factor, $Z$, of a gas is given as $Z=\frac{pV}{nRT}$

A What is the value of $Z$ for an ideal gas?

B For real gas what will be the effect on the value of $Z$ above Boyle’s temperature?

Answer 1

The value of $Z$ for an ideal gas is always $1$ because we know, ideal gas equation,

$pV=nRT$ ……$\left(1\right)$

And $Z=\frac{pV}{nRT}$ ……….$\left(2\right)$

On putting the value of $pV$ from equation $\left(1\right)$ in the equation $\left(2\right)$ of compressibility factor formula:

$Z=\frac{pV}{pV}$

$Z=1$.


Boyle’s temperature can be defined as the point in the temperature range in which a real gas starts to behave like an ideal gas at a pressure range.Above Boyle’s temperature, $pV$ is greater than $nRT$ for real gases.

So, the value of $Z$ will also be greater than $1$ ( i.e., $Z>1$ ) . Hence, for a real gas, above Boyle’s temperature, gas shows positive deviation.