Page 66 - Physical Chemistry

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The pressure dependence of c was omitted because P is held fixed for the process. Section 2.4
P
The quantity mc is the heat capacity at constant pressure C of the body: C mc . The First Law of Thermodynamics
P
P
P
P
From (2.31) we have
C dq >dT (2.33)
P
P
Equation (2.30) is more accurately written as
2 T 2 1 T f
m c 1T2 dT m c 1T2 dT q P (2.34)
P2
P1
T f T 1
If the dependence of c P2 and c P1 on T is negligible, (2.34) reduces to (2.30).
We gave examples in Sec. 2.2 of reversible and irreversible ways of doing work
on a system. Likewise, heat can be transferred reversibly or irreversibly. A reversible
transfer of heat requires that the temperature difference between the two bodies be
infinitesimal. When there is a finite temperature difference between the bodies, the heat
flow is irreversible.
Two bodies need not be in direct physical contact for heat to flow from one to the
other. Radiation transfers heat between two bodies at different temperatures (for ex-
ample, the sun and the earth). The transfer occurs by emission of electromagnetic
waves by one body and absorption of these waves by the second body. An adiabatic
wall must be able to block radiation.
Equation (2.32) was written with the implicit assumption that the system is closed
(m fixed). As is true for work, the meaning of heat is ambiguous for open systems.
(See R. Haase, Thermodynamics of Irreversible Processes, Addison-Wesley, 1969,
pp. 17–21, for a discussion of open systems.)

2.4 THE FIRST LAW OF THERMODYNAMICS
As a rock falls toward the earth, its potential energy is transformed into kinetic energy.
When it hits the earth and comes to rest, what has happened to its energy of motion?
Or consider a billiard ball rolling on a billiard table. Eventually it comes to rest. Again,
what happened to its energy of motion? Or imagine that we stir some water in a
beaker. Eventually the water comes to rest, and we again ask: What happened to its
energy of motion? Careful measurement will show very slight increases in the tem-
peratures of the rock, the billiard ball, and the water (and in their immediate sur-
roundings). Knowing that matter is composed of molecules, we find it easy to believe
that the macroscopic kinetic energies of motion of the rock, the ball, and the water
were converted into energy at the molecular level. The average molecular transla-
tional, rotational, and vibrational energies in the bodies were increased slightly, and
these increases were reflected in the temperature rises.
We therefore ascribe an internal energy U to a body, in addition to its macroscopic
kinetic energy K and potential energy V, discussed in Sec. 2.1. This internal energy con-
sists of: molecular translational, rotational, vibrational, and electronic energies; the rel-
2
ativistic rest-mass energy m c of the electrons and the nuclei; and potential energy of
rest
interaction between the molecules. These energies are discussed in Sec. 2.11.
The total energy E of a body is therefore
E K V U (2.35)

where K and V are the macroscopic (not molecular) kinetic and potential energies of
the body (due to motion of the body through space and the presence of fields that act
on the body) and U is the internal energy of the body (due to molecular motions and
intermolecular interactions). Since thermodynamics is a macroscopic science, the