Basic Chemical Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 16

2.2.2 F IRST L AW OF T HERMODYNAMICS
The universal principle of conservation of energy is the first law of thermodynamics.
According to the first law, for any closed system the change in total energy (kinetic
energy

internal energy) is the sum of the heat absorbed from its
surroundings and the work done by the system . For macroscopic changes in a closed
system with kinetic energy E K , potential energy E P , and internal energy U , and that
which absorbs heat q and does work equivalent to w , the first law can be written in
the following form:

+ potential energy +

Δ E P + Δ E K + Δ U = q − w . (2.1)

For a macroscopic system at rest, we have both Δ E P and Δ E K equal to zero. If δ q

represents the infinitesimal heat absorbed from the surroundings and −δ w represents

the infinitesimal work done by the system (by definition, w is the infinitesimal

work done on the system), then the infinitesimal change in energy d U is given by

+δ

d U = δ q − δ w . (2.2)

Notice that in the above equation we have used instead of d to remind us that q and w

are defined only for a given path of change; that is, the values of q and w are dependent
on how we reached the particular state of the system. d U , however, is independent of
the path taken by the system and is determined only by the initial and final states of
the system. One measures only changes in energies as a result of a change in the state
of the system and not the absolute energies. Thus, for a system at rest and for finite
macroscopic changes in q and w ,wehave

δ

Δ U = q − w . (2.3)

The work term in the above equation can involve any of the following: pressure-
volume work ( w PV ) and any of the other forms of shaft work, w shaft (e.g., push-pull,
electrical, elastic, magnetic, surface, etc.). When the work done by a system is only
work of expansion against an external pressure, P ext , then w is given by ∗

V 2

w = P ext d V = P ext Δ V . (2.4)

V 1

For an adiabatic process, q w , whereas for a process such

as a chemical reaction occurring in a constant-volume container,

= 0 and hence Δ U =−

Δ V = 0 and hence

Δ q . Most environmental processes are constant-pressure processes and hence

they invariably involve PV work. An example of an adiabatic process in the environ-
ment is the expansion of an air parcel and the attendant decrease in temperature as
it rises through the atmosphere, leading to what are called dry and moist adiabatic
lapse rates (see Example 2.1).
For open systems there is an additional contribution due to the flow of matter,
d U matter , and therefore we have

U =

d U = δ q − δ w + d U matter . (2.5)

∗ Note that we will henceforth drop the subscript on P .