The first law of thermodynamics is essentially the statement of the principle of the conservation of energy for thermodynamical systems.
It may be expressed by stating that the variation in energy of a system during any transformation is equal to the amount of energy that the system receives from its environment.
In purely mechanical conservative systems, the energy is equal to the sum of the potential and the kinetic energies, and hence is a function of the dynamical state of the system; because knowing the dynamical state of the system is equivalent to knowing the positions and velocities of all the mass-points contained in the system.
If no external forces are acting on the system, the energy remains constant.
Thus, if and are two successive states of an isolated system, and and are the corresponding energies, then .