Page 98 - Physical Chemistry

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Finally, about 1850, Rudolph Clausius and William Thomson (Lord Kelvin) corrected
Section 3.1
Carnot’s work to conform with the first law of thermodynamics. The Second Law of Thermodynamics
Carnot died of cholera in 1832 at age 36. His unpublished notes showed that he believed
the caloric theory to be false and planned experiments to demonstrate this. These planned
experiments included the vigorous agitation of liquids and measurement of “the motive
power consumed and the heat produced.” Carnot’s notes stated: “Heat is simply motive
power, or rather motion, which has changed its form. . . . [Motive] power is, in quantity,
invariable in nature; it is . . . never either produced or destroyed. . . .”
There are several equivalent ways of stating the second law. We shall use the fol-
lowing statement, the Kelvin–Planck statement of the second law of thermody-
namics, due originally to William Thomson and later rephrased by Planck:
It is impossible for a system to undergo a cyclic process whose sole effects are the
flow of heat into the system from a heat reservoir and the performance of an
equivalent amount of work by the system on the surroundings.
By a heat reservoir or heat bath we mean a body that is in internal equilibrium at
a constant temperature and that is large enough for flow of heat between it and the sys-
tem to cause no significant change in the temperature of the reservoir.
The second law says that it is impossible to build a cyclic machine that converts
heat into work with 100% efficiency (Fig. 3.1). Note that the existence of such a ma-
chine would not violate the first law, since energy is conserved in the operation of the
machine.
Like the first law, the second law is a generalization from experience. There are
three kinds of evidence for the second law. First is the failure of anyone to construct a
machine like that shown in Fig. 3.1. If such a machine were available, it could use the
atmosphere as a heat reservoir, continuously withdrawing energy from the atmosphere
and converting it completely to useful work. It would be nice to have such a machine,
but no one has been able to build one. Second, and more convincing, is the fact that
the second law leads to many conclusions about equilibrium in chemical systems, and
these conclusions have been verified. For example, we shall see that the second law
shows that the vapor pressure of a pure substance varies with temperature according
to dP/dT H/(T V), where H and V are the heat of vaporization and the vol-
ume change in vaporization, and this equation has been experimentally verified. Third,
statistical mechanics shows that the second law follows as a consequence of certain
assumptions about the molecular level.
The first law tells us that work output cannot be produced by a cyclic machine
without an equivalent amount of energy input. The second law tells us that it is
impossible to have a cyclic machine that completely converts the random molecu-
lar energy of heat flow into the ordered motion of mechanical work. As some wit
has put it: The first law says you can’t win; the second law says you can’t break
even.
Note that the second law does not forbid the complete conversion of heat to work
in a noncyclic process. Thus, if we reversibly and isothermally heat a perfect gas, the
gas expands and, since U 0, the work done by the gas equals the heat input
[Eq. (2.74)]. Such an expansion, however, cannot be made the basis of a continuously
operating machine. Eventually, the piston will fall out of the cylinder. A continuously
operating machine must use a cyclic process.

Figure 3.1
Cyclic
Heat Heat q machine Work done by system = q A system that violates the second
Reservoir law of thermodynamics but not the
(system)
first law.