Halliday, Resnick & Walker — The Kinetic Theory of Gases: Problem 87

Work in adiabatic expansion. Determine the work done by any ideal gas (monatomic, diatomic, or polyatomic) during an adiabatic expansion from volume \(V_i\) and pressure \(p_i\) to volume \(V_f\) and pressure \(p_f\) by applying \(W = \int p \, dV\) and \(pV^\gamma = \text{a constant}\). (b) Show that the result is equivalent to \(-\Delta E_{\text{int}}\), where the change in internal energy is given by \(\Delta E_{\text{int}} = nC_V \Delta T\).