2.15 Conservation of energy
The law of conservation of energy^{13} states that the total energy of an isolated system remains constant over time. Energy is not created or destroyed, but is transformed from one form to another. If we consider mechanical and thermal energy, it can be expressed by

(2.51) 
The rate of change of these combined energies is due to the input of mechanical power and heat from both surface ﬂuxes and internal sources.
Mechanical power is calculated by the inner product of force and . The power over a surface segment is , representing a change in strain energy. The internal power source is , representing a change in potential energy due to general body forces.
Heat is provided by an internal source of strength per unit mass and a surface heat per unit surface area. The surface heat ﬂux relating to heat input takes a negative sign, , since follows the convention of pointing out of the volume.
Equation 2.51 is derived by equating integrals of rate of change of energy to the mechanical power and heat input and taking inside the volume integral since is constant in time, as follows:

(2.52) 

(2.53) 