Page 79 - Modern physical chemistry

68 The First Law for Energy

dE=dq+dw=dq-P ex dV. [4.20]

If, in addition, the volume is kept constant (the isochoric condition), no P-Vwork is
done and (4.20) reduces to
[4.21 ]

Here as before, the subscript indicates the variable held constant. For a finite process,
we have
[4.22J
Heat absorbed at constant volume goes to increase the internal energy E of the system.
When the external pressure Pex is kept constant, the internal pressure P tends to stay
fixed and equal to it. Then (4.20) rearranges to

dqp =dE+PdV. [4.23]
With P constant, this equation yields the relation

dqp =dE +d(PV)=d(E +PV). [4.24]
Since E, P, and V are functions of state, the enthalpy

H=E+PV. [4.25]
is also. With definition (4.25), equation (4.24) reduces to
dqp =dH. [4.26]
For a finite process, we have
MI=qp. [4.27J
Heat absorbed at constant pressure goes to increase the enthalpy H of the system.
Whether or not a given system is kept at constant pressure, it possesses the property
H defined by (4.25). Over an infinitesimal change,

[4.28]

and over a finite change,
[4.29]

When the system consists of n moles ideal gas kept at a given temperature, the last
term is zero and
[4.30]

Example 4.2

What is the significance of the PV term in the enthalpy?
The work needed to make a hole of volume V in a fluid with a constant pressure P is

w= s: PdV=PS: dV=PV.
So when a system of volume V is inunersed in such a fluid (gas or liquid), it seemingly
possesses this energy.
Indeed, expanding the system by volumed V requires the energy ,1(PV). On contract-
ing to the original volume, this energy is reclaimed. Thus, PV is the energy a system
appears to possess because it fills the volume V in a surrounding fluid at pressure P.