Page 74 - Modern physical chemistry

4

The First Law for Energy

4.1 Independent Thermodynamic Variables
TO CHARACTERIZE THE MACROSCOPIC STATE OF A SYSTEM, a person needs a
complete set of independent variables. For a uniform pure substance at rest at a given
height in the gravitational field, three are needed. These may be pressure P, temperature
T, and number of moles n, set (P, T, n), or volume V, temperature T, and number of moles
n, set (V, T, n).
But temperature T is a thermal variable proportional to the mean translational energy
per molecule in an ideal gas thermometer at equilibrium with the system. As a conse-
quence, it need not be uniquely determined by the macroscopic mechanical variables P
and V. So P, V, and n, which make up set (P, V, n), are not generally suitable as inde-
pendent variables. In the next chapter, a conjugate thermal variable S will be introduced.
It may be substituted for T in the acceptable sets.
For impure materials and solutions at a given P and T, or at a given V and T, the
amount of each chemical component is independent. For the ith component, this amount
is measured by its number of moles n i •
To relate different states, one employs processes. Of particular interest are those that
are carried out reversibly. By definition, a process is reversible if its direction can be reversed
at any stage by some infinitesimal shift in one or more of the independent variables.
The energy of a system may be broken down into (a) that due to its position and ori-
entation in an externally imposed field, (b) that due to translation of its center of mass,
(c) that due to the volume it displaces in surrounding material, and (d) that due to the
relative positions and motions of the particles composing it. Part (d) is called the inter-
nal energy E of the system.
4.2 Work

In mechanics, the work done by a force F acting over a displacement ds equals the
component of the force in the direction of the displacement times the displacement, the
scalar product
dw=F·ds=F x dx+Fy dy+Fzdz. [4.1 ]
Here F,,,, Fy , Fz are the components of the force for the rectangular coordinate changes
dx, dy, dz.

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