Question

In a gas equation, for one mole of real gas $\left(p+\frac{a}{V^{2}}\right)(V-b)=R T$ dimensions of constants $a$ and $b$ are :

• A. $\left[L^{2}\right],\left[M L^{4} T^{-2}\right]$
• B. $[L],\left[M L^{2} T^{-2}\right]$
• C. $\left[M L^{5} T^{-2}\right],\left[L^{3}\right]$
• D. none of these

Answer 1

Answer: (C)

We know that only dimensions of similar quantities can be added or subtracted. Given, $\left(P+\frac{a}{V^{2}}\right)(V-b)=R T$
Dimensions of $V =$ Dimensions of $b [b]=\left[L^{3}\right]$
Dimensions of $\frac{a}{V^{2}}$ =Dimensions of pressure $P$
$\Rightarrow $ Dimensions of $a=$ Dimensions of $P \times V^{2}$
Dimensions of $[a]=\left[M L^{-1} T^{-2}\right]\left[L^{6}\right]$
$\Rightarrow [a]=\left[M L^{5} T^{-2}\right]$