Page 31 - Bruno Linder Elementary Physical Chemistry

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

16 Elementary Physical Chemistry

Note: U is a state function, meaning it is independent of the previous
history of the system but depends only on the current state and not
on the way the state was formed. The quantities q and w are not state
functions.
There are other state functions, to be introduced later. All will be
denoted by capital letters in contrast to the concepts of work and
heat, which are denoted by small letters.

2.8. Exact and Inexact Differentials
The First Law is frequently expressed in differential form:

dU =dq +dw (2.9)
There is a difference between the differentials dU on the one hand and
dq and dw on the other hand. dU is an exact differential — its integral
depends only on the initial and final states of the system and not on the
path of integration. The differentials dq and dw are generally not exact.
Their integrated values depend on the path of integration.
As an illustration of the meaning of exact and inexact differentials,
consider the integration of ydx (the horizontally shaded area) between the
limits A and B. Obviously, the value depends on the path of integration. The
same is true for the integral xdy. But the sum of these two is independent
of the path. This shows that individual integrals may be path-dependent,
but their sum could be path-independent (see Fig. 2.2).

Graphical representation of the sum of the integrals ∫ydx + ∫xdy.
Fig. 2.2