Page 11 - Partition & Adsorption of Organic Contaminants in Environmental Systems

2 IMPORTANT THERMODYNAMIC PROPERTIES

and pressure (where there is no net exchange of mass) is governed by the
equality or inequality of its chemical potentials with the (various) phases. The
chemical potentials being referred to are the molar Gibbs free energies of
the component in individual phases. There is a natural tendency of a chemi-
cal to come to a state of equilibrium between all contacted phases, where the
chemical potential gradient across phase boundaries is zero. The chemical
potentials are derived from the first and second laws of thermodynamics. In
the derivation of Gibbs free energy, the reader will also be introduced to two
other important thermodynamic properties, enthalpy (heat) and entropy, by
which one can distinguish a surface process from a solution process, as shown
later. For a more detailed treatment of the thermodynamic quantities and their
relationships, the reader is directed to a physical chemistry textbook.

1.2 FIRST LAW OF THERMODYNAMICS

The first law of thermodynamics is a consequence of the principle of conser-
vation of energy: that is, that heat, kinetic energy, potential energy, and elec-
trical energy are different forms of energy that can be interconverted but can
be neither created nor destroyed. Consider any system enclosed in a vessel
that can change its volume and exchange heat with its surroundings but is
impervious to the passage of matter. We postulate a property called the inter-
nal energy of the system, E. We will be concerned with the change in E and
not with its absolute value. If the system absorbs an amount of heat q with no
other changes, the conservation of energy requires that its internal energy
increase by the amount of q; conversely, the internal energy will decrease by
the amount of q if an amount of heat q is released to its surroundings. Simi-
larly, if the system does work w on its surroundings with no other changes, its
internal energy will decrease by the amount of w. If the system both exchanges
heat and does work, the change in internal energy is then

-
DE = q w (1.1)
where q is here taken as positive for heat absorbed by the system and w as
positive for work done by the system. The first law also implies that E is a state
function: that its magnitude is solely dependent on its state variables (e.g., tem-
perature, pressure, and volume). For any series of processes that end with a
return to the original state variables, DE = 0.
For a constant-pressure system involving only the work of expansion and
contraction (i.e., no electrical work), w equals PDV, where P is the (constant)
pressure and DV is the (finite) change in volume. In this case, the change in E
is therefore

DE = q - P DV (1.2)