INTERNAL energy is given by, \(\Delta U = m{c_v}\Delta T\)Calculation:Given:V2 = 2V; V1 = V, and P1 = P2 = P\(\Delta U = m\frac{R}{{\gamma - 1}}\LEFT( {{T_2} - {T_1}} \right)\)where \({C_v} = \frac{R}{{\gamma - 1}}\) and ΔT = T2 – T1\(\Delta U = \frac{1}{{\gamma - 1}}\left( {mR{T_2} - mR{T_1}} \right)\)As we know from the ideal gas equation PV = mRT.\(\Delta U = \frac{1}{{\gamma - 1}}\left( {{P_2}{V_2} - {P_1}{V_1}} \right)\)\(\Delta U = \frac{P}{{\gamma - 1}}\left( {{}{2V} - {}{V}} \right)\)∴ we GET, \(\Delta U = \frac{{PV}}{{\gamma - 1}}\).