Question

The pressure of a gas $P=\frac{RT}{v-b}{e}^{\left(\frac{-aV}{RT}\right)}$. If $V$ be the volume of gas, $R$ be the universal gas constant and $T$ be the absolute temperature then the dimensional formula of '$a$' is same as that of:

• A. $V$
• B. $P$
• C. $T$
• D. $R$

Answer 1

Answer: (B)

$P$

$\frac{aV}{RT}$ should be dimensionless.
$a=\frac{RT}{V}$
Since $P=\alpha \frac{RT}{V-b}\Rightarrow \frac{RT}{V}=P$
$\Rightarrow a=P$ i.e. Dimension of $a$ should be equal to $P$.