*Question: What are the units of
? What are the units of
?*

Imagine that there is a completely homogeneous system that has been arbitrarilry divided into small volumes of size :

Consider what is left of the internal energy after we subtract off the ``mechanical'' or ``compression'' energy:

(11-12) |

The reason that the integration can be carried out is that both and are extensive variables and are thus additive for each subsystem.

So that we can define a new state function (that is also extensive),

(11-13) |

It is sensible to interpret as the ``thermal energy'' at constant pressure. In other words, we divide the internal energy for a simple fluid into two parts--one part corresponding to that stored as compressive energy ( ) and another part the thermal energy . Another way to see this is:

(11-14) |

In other words

(11-15) |

for an ideal gas:

(11-16) |