Interne energie

The internal energy of a system can be defined as the sum of the kinetic and potential energies of all the individual atoms in the system.

Consider a system of a monoatomic ideal gas. When the gas is heated at constant volume, the kinetic energy of the atoms increases, but since there is no interaction between the atoms, their potential energy remains zero.

Therefore, the internal energy depends on the average kinetic energy of the monoatomic atoms. It is expressed as three over two Nk_BT, where N is the number of gas atoms, k_B is the Boltzmann constant, and T is its temperature. Thus, the internal energy of an ideal gas at constant volume depends only on temperature.

The internal energy of a system is a state function. Boiling water that has been cooled to room temperature has the same internal energy as water obtained by melting ice to room temperature.

Thus, the internal energy depends only on the state of the system, not on the path employed to obtain it. Therefore, it is path-independent.