The equation $\left(P+\dfrac{a}{v^{2}}\right)(v-b)=\text{constant}$. The units of $a$ are:

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Question: The equation $\left(P+\dfrac{a}{v^{2}}\right)(v-b)=\text{constant}$. The units of $a$ are: [PMT/NEET-1995]
a. Dyne × cm$^5$
b. Dyne × cm$^4$
c. Dyne/cm$^3$
d. Dyne/cm$^2$

Answer: b. Dyne × cm$^4$

Solution: From van der Waals form

$(P + a/v^{2})(v-b)=\text{constant}$.

Term $a/v^{2}$ must have units of pressure $P$ (dyne/cm$^2$ in CGS), so

$[a]=[P][v^{2}]=(\text{dyne cm}^{-2})(\text{cm}^{6})=\text{dyne cm}^{4}$.