The volume of a cylinder is equal to the area of its base multiplied by its height. So \(A\ell_{\mathrm{i}}\) and \(A\ell_{\mathrm{f}}\) are, respectively, the initial volume \(V_{\mathrm{i}}\) and final volume \(V_{\mathrm{f}}\) occupied by the gas, and we can rewrite Equation 15-3 as
(15-1) \(\ \ \ \ Q = \Delta{U} + W\)
It’s conventional to rearrange this equation with \(\Delta{U}\) on one side and \(Q\) and \(W\) on the other side: