Page 12 - Partition & Adsorption of Organic Contaminants in Environmental Systems

SECOND LAW OF THERMODYNAMICS 3

If one defines a new state function, H, called enthalpy,as

H = E + PV (1.3)

then the change in H at constant pressure will be

DH = DE + P DV (1.4)

A comparison of Eqs. (1.2) with (1.4) leads to

DH = q for a constant-pressure process (1.5)

The enthalpy is therefore a useful state function for describing the heat
exchange at constant pressure.

1.3 SECOND LAW OF THERMODYNAMICS

We first begin with the concept of a reversible process in thermodynamics. In
addition to the usual sense of a reversible process, the condition of thermo-
dynamic reversibility for any process is that it proceeds at all times infini-
tesimally close to equilibrium, so that its direction can be reversed by an
infinitesimally small change in one or more of the state variables. A close
approximation to a reversible process is the freezing of water in a vessel main-
tained below but very close to the equilibrium freezing point (which is 0°C at
1 atmosphere); the process can be reversed by raising the temperature very
slightly above the freezing point. Conversely, the freezing process of super-
cooled water can be carried out irreversibly by seeding it with an ice crystal.
In the reversible expansion of a gas against a resistance that is close to the
gas pressure at all times, the differential work is PdV and the overall work is
ÚPdV. By contrast, in the extreme case of the gas expanding into a vacuum,
the work is zero.
The most useful statement of the second law of thermodynamics is
described in terms of a state function called the entropy (S), which is a measure
of the degree of randomness or disorder in a system. For a system undergo-
ing a change in state, the change in entropy is such that

dS = dq T for an infinitesimal reversible process (1.6)

dS > dq T for an infinitesimal spontaneous process (1.7)

where T is the thermodynamic temperature [Kelvin (K)]. For a reversible
process, dq = TdS. By relating Eq. (1.6) to the first law, one finds for a
reversible process in a closed system that involves only the P–V work (i.e., no
electrical work) that