Question

In the equation $(P+\frac{a}{V^2})(V-b)$ = constant P is the pressure, V is the volume and a and b are constants. The unit of a is:

• A. $\text{dyne}\times c{m}^5$
• B. $\text{dyne}\times c{m}^4$
• C. $\text{dyne}\times c{m}^{-3}$
• D. $\text{dyne}\times c{m}^2$

Answer 1

The correct option is D $\text{dyne}\times c{m}^2$

According to given equation, the terms $P$ and $\frac{a}{V^2}$ wil have the same dimension because only the units with same dimensions can be added.

So, the dimension of $\frac{a}{V^2}$ is same as that of pressure.

$\frac{a}{V^2}=P$

$a=P{V}^2$

so, the unit of $a$ is $dyne\times c{m}^2$