# Energy density and inernal density relations

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 $\epsilon = \rho / c ^2 + €$?

• It would help a lot if you explained what you denote by $\epsilon$, $\rho$, $c$ and $€$. – Prof. Legolasov Nov 10 '16 at 5:45
• epsilon = energy density , rho= rest mass density, c =speed of light, e=internal energy – umar khan Nov 10 '16 at 14:32
• In this case your formulas are incorrect on dimensional grounds (did you mean $\epsilon = \rho c^2$?). What is "internal energy"? – Prof. Legolasov Nov 10 '16 at 14:49
• 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. – N0va Nov 10 '16 at 18:44

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