Environmental Engineering Reference
In-Depth Information
enthalpy
(
h
) and is defined as
h
≡
e
+
p
v
(3.13)
The enthalpy has a simple physical interpretation. Suppose a unit mass of material is surrounded by
an environment in which the pressure is fixed and equal to the pressure
p
of the system. If a small
amount of heat,
dq
, is added to the system, its temperature will rise and it will expand, undergoing
an increment of volume
d
on the environment.
According to the first law, equation (3.7), the heat and work amounts change the energy
e
:
v
and performing an amount of work
d
w
=
pd
v
de
=
dq
−
pd
v
dq
=
de
+
pd
v
=
de
+
d
(
p
v)
=
d
(
e
+
p
v)
=
dh
where the equality
pd
follows from the constancy of
p
in this process. Thus the amount
of heat added in a constant pressure process is equal to the increase in enthalpy of the material. The
ratio of the increase in enthalpy, at fixed pressure, to the increment of temperature experienced in
this process is called the
constant-pressure specific heat
and is given the symbol
c
p
,
5
v
=
d
(
p
v)
∂
h
{
p
,
T
}
c
p
≡
(3.14)
∂
T
p
When we consider a similar heating at fixed volume, no work is done and the increase in energy
de
is equal to the heat increment
dq
. The ratio of the energy increase to the concomitant temperature
increase is called the
constant-volume specific heat, c
v
,
∂
{
v,
}
e
T
c
v
≡
(3.15)
∂
T
v
A second property that will be found useful is the
Gibbs' free energy,
given the symbol
f
and
defined by
f
≡
h
−
Ts
=
e
+
p
v
−
Ts
(3.16)
For a process that proceeds at constant temperature and pressure, the second law of thermodynamics
requires that the amount of work done by a system cannot exceed the reduction of free energy
f
. The
free energy is a useful thermodynamic function in cases of chemical or phase change. For example,
a sample of liquid water and water vapor can be held in equilibrium at the boiling temperature
corresponding to the sample pressure. If heat is added while the pressure remains fixed, some
liquid is converted to vapor but the temperature remains unchanged. For this heat transfer process
at fixed temperature and pressure, the free energy
f
is unchanged. In Section 3.12 we shall use the
free energy to determine the limiting performance of electrochemical cells.
5
In this expression,
h
{
p
,
T
}
is considered a property depending upon the pressure
p
and temperature
T
. The
partial derivative
∂
h
/∂
T
is taken with respect to
T
holding
p
fixed. A similar constraint is implied in equation
(3.15) below, where
e
{
v,
T
}
is a function of volume
v
and temperature
T
.
