Halliday, Resnick & Walker — The Kinetic Theory of Gases: Problem 54

We know that for an adiabatic process \(pV^\gamma = \text{a constant}\). Evaluate "a constant" for an adiabatic process involving exactly 2.0 mol of an ideal gas passing through the state having exactly \(p = 1.0 \text{ atm}\) and \(T = 300 \text{ K}\). Assume a diatomic gas whose molecules rotate but do not oscillate.