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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 $\epsilon = \rho / c ^2 + €$?

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  • $\begingroup$ It would help a lot if you explained what you denote by $\epsilon$, $\rho$, $c$ and $€$. $\endgroup$ – Prof. Legolasov Nov 10 '16 at 5:45
  • $\begingroup$ epsilon = energy density , rho= rest mass density, c =speed of light, e=internal energy $\endgroup$ – umar khan Nov 10 '16 at 14:32
  • $\begingroup$ In this case your formulas are incorrect on dimensional grounds (did you mean $\epsilon = \rho c^2$?). What is "internal energy"? $\endgroup$ – Prof. Legolasov Nov 10 '16 at 14:49
  • $\begingroup$ The rest mass density $\rho$ for an one particle fluid or gas is given by: $$\rho= m n,$$ where $n$ is the particle number density and $m$ is the particle mass. The energy density $\epsilon$ of such a system is in general not $\epsilon\neq\rho c^2$. $\rho c^2$ is still the rest mass density just expressed in units of an energy density. Energy density includes things like binding energy or if you want thermal/kinetic energy. How the energy density is related to number density strongly depends on the system. $\endgroup$ – N0va Nov 10 '16 at 18:44
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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).

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