## 23 The Components of the Rest Energy of an Amount of Gas

The total energy *E* of an ideal gas, enclosed in the volume *V* at the pressure *P* , is the sum of three terms:

*E* j = *M · c*^{2} + *U *j+* jP · V* j = *M · c*^{2} + * H *

The meaning of those terms is the following:

*M · c*^{2}=*N · m · c*^{2}is the rest energy of the gas due to the*mass*of the particles*U*is the*heat content*or the*thermal energy*of the gas, frequently called 'internal energy'. In an ideal gas*U*is one and the same as the kinetic energy of the particles due to their motion relative to the center of mass of the gas. There is no energy stored in rotations or vibrations of the molecules*P · V*is the so-called*thermodynamic work*of the gas. It is the work required to 'shovel free' the volume*V*for the gas against the external pressure*P*. Imagine this energy being stored as potential energy in the tension of the vessel containing the gas

The enthalpy* H* = *U* + *P · V * is the sum of thermal and mechanical energy contained in the 'hot' gas. *H* is ( as *U* and *P · V* ) an extensive state variable

( cf. sections **1** and **35** ).