Consider a gas, of infinite extent, divided into regions \(A\) and \(B\) by an imaginary sheet running through the system. The molecules of the gas interact through a potential energy function \(u(r)\). Show that the average net force \(\boldsymbol{F}\) experienced by all the molecules on the \(A\)-side of the sheet caused by all the molecules on the \(B\)-side are perpendicular to the plane of the sheet, and that its magnitude (per unit area) is given by

\[\frac{F}{A}=-\frac{2 \pi n^{2}}{3} \int_{0}^{\infty}\left(\frac{d u}{d r}ight) g(r) r^{3} d r\]