where the line over the velocity term indicates that the average value is calculated over the entire ensemble. The total thermal energy of the sample is proportional to the macroscopic temperature by a constant factor accounting for the three translationa

where the line over the velocity term indicates that the average value is calculated over the entire ensemble. The total thermal energy of the sample is proportional to the macroscopic temperature by a constant factor accounting for the three translational degrees of freedom of each particle and the Boltzmann constant, converting units between the microscopic model and the macroscopic temperature. This formalism is the basic assumption that directly yields the ideal gas law, and it shows that for the ideal gas, the internal energy consists only of its thermal energy