Page 29 - Bruno Linder Elementary Physical Chemistry

August 25, 2010 9:36 9in x 6in b985-ch02 Elementary Physical Chemistry

14 Elementary Physical Chemistry

2.5. Reversible Process

When the internal pressure P is equal to the external one P ext, the system
is said to be in a state of equilibrium. An infinitesimal increase in P ext will
result in an increase in compression and an infinitesimal decrease in P ext
will result in an increase in expansion. A reversible process is a process
which proceeds through a succession of equilibrium states.
If an ideal gas is in equilibrium with its surroundings, then P ext = P
and, for an ideal gas, P = nRT/V . Therefore, the work (done by the
surrounding on the system) in a reversible change is

w PV = −∫(nRT/V )dV = −nRT ln V f /V i (2.4)
Note again that the work is positive in a compression (V f <V i ) and negative
in an expansion (V f >V i ).

2.6. Measurement of Heat
The traditional way to discuss the concepts of temperature and heat is
to define one of these and deduce the other from it. Attempts to define
temperature in terms of heat are bound to cause difficulties since normally
heat is not observed directly but inferred from changes in temperature.
Statements such as radiant energy, thermal heat flow, are sometimes used
in defining heat. Using such descriptions of heat to define temperature is
obviously not very satisfactory and will be avoided here.

Comment: The concept of heat is most conveniently described in
terms of the heat capacity, which is the heat divided by the
temperature change (Section 10). Here, we introduce the concept by
focusing directly on temperature changes of two systems in thermal
equilibrium.

Consider a system, A, initially at a temperature T A in equilibrium with
a system, B, whose initial temperature is T B . If the equilibrium temperature
is T , small changes in temperature of the two systems can be written as
dT A = T − T A and dT B = T − T B . The ratio of these quantities defines the
ratio of the heat capacities,thatis

dT A /dT B = −C A /C B (2.5)