When an ideal gas undergoes a temperature change at constant volume, its energy changes by ∆U = Cv, ∆T

(a) Explain why this result holds for an ideal gas for any temperature change independent of the process.

(b) Show explicitly that this result holds for the expansion of an ideal gas at constant pressure by first calculating the work done and showing that it can be written as W = nR∆T, and then by using ∆U = Q W, where Q = Cp ∆T.