A refresher on thermodynamics - Geochemistry: An Introduction - page 304

C

Appendix C A refresher on thermodynamics

The first principle postulates the existence of a conservative quantity, energy. Energy exists
in several forms: chemical bonds, thermal agitation of ions and molecules (the sum of
these two giving the internal energy U ), potential energy, kinetic energy, etc. Energy can
be transferred in several ways, by heat transfer

δ

Q (propagation of agitation) or mechanical

δ

work W (exchange of a quantity of motion with a pressure agent, such as the atmosphere

or the weight of a column of rock). The first principle can be written in simplified form as:

d U = δ Q + δ W = δ Q − P d V (C.7)

where P is pressure and V is the volume of the system. Heat Q and work W are not
themselves conservative properties.
The second principle of thermodynamics states that an isolated system drifts spon-
taneously toward the most probable state, i.e. a state in which a maximum number of
equivalent microscopic configurations are available to it. The measure of the number of
equivalent configurations accessible to a system is its entropy S . The entropy of an isolated
system can therefore only increase. However, possible arrangements of a system can be
added or removed by adding or subtracting energy, as in a game of checkers where the
potential for varied situations depends on the number of pieces that can be arranged on the
board. For a pure heat exchange at constant volume, we write:

= δ

Q
T + σ

d S d t (C.8)

where the variable T , defined by this equation, refers to the absolute temperature (in
kelvins) of the system, t to time, and

to the entropy production by dissipative processes,
such as shear heating and chemical diffusion. According to the second principle,

σ

σ must be

non-negative. For an infinitesimal reversible transformation, is zero. For a system whose

state is controlled by prescribing its entropy S and its volume V , the variation in energy is
described by the variation in internal energy U such that:

σ

d U ≤ T d S − P d V (C.9)

the relation of which is reduced to an equality in the case of a reversible transformation.
In ( U , S , V ) space, the entropy of a system whose energy remains constant evolves spon-
taneously toward a maximum ( Fig. C.1 ) . The system's geometry shows that an adiabatic
system ( 0) evolves spontaneously toward a minimum internal energy U .

For a system whose control variables are entropy and pressure, we use enthalpy H

δ Q =

=

U + PV . In a calorimeter (d S = 0) of constant volume, the change in thermal energy is