Question

A gas is said to behave like an ideal gas when the relation $\frac{pV}{T}$ = constant. When do you expect a real gas to behave like an ideal gas?

• A. When the temperature is low
• B. When both the temperature and pressure are low
• C. When both the temperature and pressure are high
• D. When the temperature is high and pressure is low

Answer 1

Answer: (D)

As we know that the van der Waals' equation is
$\left(p+\frac{a}{V^2}\right)(V-b)=RT$
The real gases show ideal behaviour when pressure approaches zero and temperature is high. At this condition there is no force of attraction and
repulsion between the molecules of gas.
Thus, the effect of $\frac{a}{V^2}$ and $b$ is negligible, i.e
$pV=RT$
$\frac{pV}{RT}=1$
We also know $\frac{pV}{RT}=Z$ (for ideal gas $Z=1$ )
( $Z$ is compressibility factor)
Therefore an real gas behaves like ideal gas when the temperature is high and
pressure is low.