An equation is given here $\left(P+\frac{a}{V^{2}} ight)=b \frac{ heta}{V}$ where $P=$ Pressure, $

Question

An equation is given here $\left(P+\frac{a}{V^{2}}ight)=b \frac{	heta}{V}$ where $P=$ Pressure, $V=$ Volume and $	heta=$ Absolute temperature. If $a$ and $b$ are constants, the dimensions of $b$ will be

Professor PC Thomas Classes · Answer

(b) : Equation $\left(P+\frac{a}{V^{2}}ight) V=b 	heta$. \\ Since $\frac{a}{V^{2}}$ is added to the pressure, the term $\left(P+\frac{a}{V^{2}}ight)$ has dimensions of Pressure. \\ Dimensions of $b = \frac{P 	imes V}{	heta} = \frac{\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}ight]\left[\mathrm{L}^{3}ight]}{[\mathrm{K}]} = \left[\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{~K}^{-1}ight]$