Physics

In van der Waal's equation $$\left(P+\dfrac{a}{V^{2}}\right)(V-b)=RT$$, what are the dimension of the constant of $$a$$ and $$b$$?


SOLUTION

$$\left( P+\dfrac{a}{{{V}^{2}}} \right)(V-b)=RT$$

Only the term having same unit can added.

Unit of $$\dfrac{a}{{{V}^{2}}}=pascal=N{{m}^{-2}}$$

  $$ \Rightarrow \dfrac{a}{{{\left( {{m}^{3}} \right)}^{2}}}=N{{m}^{-2}} $$

 $$ \Rightarrow a=N{{m}^{4}} $$

Unit of $$b=volume={{m}^{3}}$$

Unit of $$a=N{{m}^{4}}\ and\ b={{m}^{3}}$$ 

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