(4.7) |

where is the heat absorbed by the system. On a microscopic level, the energies of the individual microstates are unaffected by the absorption of heat. In fact, it is the distribution of the systems in the ensemble over the various microstates that is modified.

Suppose that the system
is thermally insulated from its environment. This can be
achieved by surrounding it by an *adiabatic* envelope (i.e., an envelope
fabricated out of a material that is a poor conductor of heat, such a fiber glass).
Incidentally, the term adiabatic is derived from the Greek *adiabatos*, which
means ``impassable.'' In scientific terminology, an adiabatic process is one in
which there is no exchange of heat. The system
is still capable of interacting
with its environment via its external parameters. This type of interaction is
termed *mechanical* interaction, and any change in the average energy of the
system is attributed to work done on it by its surroundings. Thus,

where is the work done by the system on its environment. On a microscopic level, the energy of the system changes because the energies of the individual microstates are functions of the external parameters. [See Equation (4.6).] Thus, if the external parameters are changed then, in general, the energies of all of the systems in the ensemble are modified (because each is in a specific microstate). Such a modification usually gives rise to a redistribution of the systems in the ensemble over the accessible microstates (without any heat exchange with the environment). Clearly, from a microscopic viewpoint, performing work on a macroscopic system is quite a complicated process. Nevertheless, macroscopic work is a quantity that is easy to measure experimentally. For instance, if the system exerts a force on its immediate surroundings, and the change in external parameters corresponds to a displacement of the center of mass of the system, then the work done by on its surroundings is simply

(4.9) |

that is, the product of the force and the displacement along the line of action of the force. In a general interaction of the system with its environment there is both heat exchange and work performed. We can write

which serves as the general definition of the absorbed heat . (Hence, the equivalence sign.) The quantity is simply the change in the mean energy of the system that is not due to the modification of the external parameters. Note that the notion of a quantity of heat has no independent meaning apart from Equation (4.10). The mean energy, , and work performed, , are both physical quantities that can be determined experimentally, whereas is merely a derived quantity.