Page 119 - Essentials of physical chemistry

5 The Second and Third Laws

of Thermodynamics

INTRODUCTION
While the first law of thermodynamics has some interesting mysteries, which are overcome using
the powerful ‘‘after-minus-before’’ principle, energy concepts are familiar to us in science. The next
important topic is all around us and taken for granted as a part of life, but most of us do not know it
can be made quantitative. It is the principle we sometimes call ‘‘Murphy’s law’’ related to the natural
tendency of disorder to increase. If you open a brand new deck of cards and drop them from waist
height, do you expect they will remain in order? Stack 10 coins heads up and drop them again from
waist height; do you expect them to land all heads up? The answer is ‘‘no’’ to both questions, so
what is going here? We are hinting strongly that while there is a natural tendency for energy to run
‘‘down hill,’’ there is another tendency in nature that tends to increase.
One of the major discoveries of thermodynamics, primarily by Boltzmann, is the way to quantify
the phenomenon of disorder beginning with his 1866 PhD thesis. Shortly before that Clausius
proposed a second law of thermodynamics in words in 1862. But first, maybe the basic concept was
discovered by Sadi Carnot in 1824 (Figure 5.1) [1].

CARNOT CYCLE=ENGINE
The second law of thermodynamics has historically been a mysterious concept, and the basic idea
has been verbalized by Clausius, Kelvin, Planck, and others for those who ‘‘think in words.’’ One
simple statement by Rudolph Clausius (1822–1888) was
Heat generally cannot flow spontaneously from a material at lower temperature to a material at higher
temperature.

The key word here is ‘‘spontaneously’’ because we know that refrigeration can move heat from cold
to hot regions, but the natural trend is for heat energy to flow from a hot environment to a cold
environment. There are many verbal variations of the second law, and a student can find a great deal
of further discussion in other texts but in keeping with the idea of Essential Physical Chemistry we
choose to pin our explanation on algebraic results from the idealized Carnot cycle (Figure 5.2).
Carnot defined a cyclic process in four steps as a process for a hypothetical engine to convert heat to
work. The process is usually described with a P, V graph. According to the ideal gas law, the
equation for ‘‘PV ¼ constant’’ leads to the positive branch of a hyperbola called an ‘‘isotherm.’’ In
the previous chapter, we carried out a model analysis of the adiabatic response of a gas to
compression and expansion. The shape of the PV curve for an adiabatic step is not an isotherm
because we know the temperature changes. Consider an adiabatic expansion of a gas. If q ¼ 0 and no
heat flows into the gas, the temperature drops, so what would have been an isotherm on the PV
graph ‘‘sags’’ to a lower temperature. Similarly, we know from the diesel engine example that
adiabatic compression with no heat flow, q ¼ 0, leads to a higher temperature, which crosses over
isotherms in the upward direction. Thus, we expect isotherms for constant temperature processes but
deviations from the perfect hyperbolic shape for adiabatic steps on a P, V graph. There is a dynamic

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