A cylinder contains 5.12 mol of an ideal gas at pressure 5.60 × 10⁵ Pa and volume 3.80 × 10⁻² m³. The average kinetic energy E_K of a molecule of the gas is given by E_K = (3/2)kT, where k is the Boltzmann constant and T is the thermodynamic temperature. The gas is heated at constant pressure so that its temperature rises by 125 K (the new volume is 4.75 × 10⁻² m³).

Calculate the increase in internal energy of the gas. Explain your working.