Question

In the equation $(P+\frac{a}{V^2})(V-b)=\text{constant}$, the unit of $a$ is

• A. ${\text{dyne}\times \text{cm}}^5$
• B. ${\text{dyne}\times \text{cm}}^4$
• C. ${\text{dyne}\times \text{cm}}^2$
• D. $\text{dyne}\times \text{cm}$

Answer 1

The correct option is B ${\text{dyne}\times \text{cm}}^4$

Given, $(P+\frac{a}{V^2})(V-b)=\text{constant}$
So, from the equation we can say that $\left[P\right]=\left[\frac{a}{V^2}\right]$
or, $a=P{V}^2=\frac{\text{dyne}}{{\text{(cm)}}^2}\times ({\text{cm}}^3{)}^2={\text{dyne}\times \text{cm}}^4$