The only form of energy possessed by molecules of a monatomic ideal gas is translational kinetic energy. From kinetic, the average kinetic energy per molecule is KEmolecule = ³⁄₂kBT = (³⁄₂) (R/NA) (T)
Use these results to show that the internal energy of a monatomic ideal gas at pressure P and occupying volume V may be written as U = ³⁄₂PV.
