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In van der Wa...

Question

In van der Waal's equation $(P + \frac{a}{V^{2}}) (V - b) = R T$ , what are the dimension of the constant of $a$ and $b$ ?

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Solution

$(P + \frac{a}{V^{2}}) (V - b) = R T$

Only the term having same unit can added.

Unit of $\frac{a}{V^{2}} = p a s c a l = N m^{- 2}$

$\Rightarrow \frac{a}{{(m^{3})}^{2}} = N m^{- 2}$

$\Rightarrow a = N m^{4}$

Unit of $b = v o l u m e = m^{3}$

Unit of $a = N m^{4} a n d b = m^{3}$

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