Energy principles for temperature varied with time

This paper discusses some extensions of energy principles in classical and continuum thermodynamics. The modified energy principles will extend the first and second laws in classical continuum thermodynamics to the case where the temperature is varied with time. it is shown that the modified energy principles are consistent with the statistical mechanics. The inertial heat and inertial entropy concepts play the kernel roles in the modified energy principles. The temperature wave equation with finite phase velocity is a natural result of the inertial entropy theory. The effect of the temperature inertia in multi-field coupling case is discussed shortly.