The equation of state of a real gas is given by where and are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of is similar to that of:

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Solution

Q.
The equation of state of a real gas is given by $(P + \frac{a}{V^{2}}) (V - b) = R T,$ where $P, V$ and $T$ are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of $\frac{a}{b^{2}}$ is similar to that of: [2024]

1 $P V$

2 $P$

3 $R T$

4 $R$

Ans.
(2)

$[P] = [\frac{a}{V^{2}}] \Rightarrow [a] = [P V^{2}]$

And $[V] = [b]$

$\frac{[a]}{[b^{2}]} = \frac{[P V^{2}]}{[V^{2}]} = [P]$

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