Energy density and internal density relations

Question

If energy density relates to rest mass density as $epsilon = rho / c^2$. How internal energy relates to energy density?
Also, when do we write $epsilon = rho / c^2$ an when $epsilon = rho / c ^2 + €$?

DilithiumMatrix · Answer

The total energy density is the sum of all the individual types of energy density, for example: rest-mass, (or thermal/`pressure'), internal energy, but may also include electromagnetic, kinetic, etc

i.e. (Eq. 1)
$$epsilon = rho c^2 + € + ...$$  Note that it is mass-density times $c^2$, not divided by.

If some of the terms on the right-hand-side are zero (like velocity, magnetic field, or internal energy) then we can simplify to,

(Eq. 2) $$epsilon = rho c^2.$$
Equation (2) is a special case of equation (1).

Energy density and internal density relations

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