3.5 The Third Law of Thermodynamics and Absolute Entropies 139Entropies 3.5 The Third Law of Thermodynamics and Absolute
Absolute Entropies
The third law of thermodynamics was first stated by Nernst:For certain isothermal
chemical reactions between solids, the entropy changes approach zero as the thermo-
dynamic temperature approaches zero. Nernst based this statement on his analysis
of experimental data obtained by T. W. Richards, who studied the entropy changes
of chemical reactions between solids as the temperature was made lower and lower.
The statement of Nernst was sometimes calledNernst’s heat theorem, although it is a
statement of experimental fact and not a mathematical theorem.Walther Hermann Nernst, 1864–1941,
was a German physical chemist who
received the 1920 Nobel Prize in
chemistry for his work on the third law
of thermodynamics. He made
numerous other contributions, including
the Nernst equation of electrochemistry.Theodor William Richards, 1868–1928,
was an American chemist who won the
1914 Nobel Prize in chemistry for his
accurate chemical determinations of
atomic masses.In 1911 Planck proposed extending Nernst’s statement to assert that the entropies of
individual substances actually approach zero as the temperature approaches zero. How-
ever, there is no experimental justification for this assertion. In 1923 Lewis proposed
the following statement of the third law: “If the entropy of each element in some crys-
talline state be taken as zero at the absolute zero of temperature, every substance has a
finite positive entropy—but at the absolute zero of temperature the entropy may become
zero, and does so become in the case of perfect crystalline substances.”^4 We base our
entropy calculations on this statement.Max Karl Ernst Ludwig Planck,
1858–1947, was a German physicist
who won the 1918 Nobel Prize in
physics for his pioneering work in
quantum theory.
Gilbert Newton Lewis, 1875–1946, was
an American chemist who made a
number of important contributions. Prior
to the development of quantum
mechanics, Lewis proposed that
covalent chemical bonds arise from
sharing of electrons according to the
octet rule. He also proposed in 1926
that the name “photon” be applied to
quanta of light.The restriction to perfect crystals was made necessary by the discoveries of Simon
and Giauque, who found that substances such as CO and NO fail to obey the third law in
their ordinary solid forms. These substances easily form metastable crystals with some
molecules in positions that are the reverse of the equilibrium positions, and ordinary
crystals are in metastable states such that their entropies do not approach zero at 0 K.
We will return to this topic later in this section.Franz Eugen (Sir Francis) Simon,
1893–1956, was a German-British
physicist who, independently of
Giauque, developed the method of
adiabatic demagnetization to reach low
temperatures.
William Francis Giauque, 1895–1982,
was an American chemist who
discovered that ordinary oxygen
consists of three isotopes. He received
the 1949 Nobel Prize in chemistry for
pioneering the process of adiabatic
demagnetization to attain low
temperatures.Exercise 3.16
Show that if the entropies of pure perfect crystalline elements are taken equal to nonzero constants
at zero temperature, the molar entropy of a pure perfect crystalline compound at zero temperature
is equal to the sum of the entropies of the appropriate numbers of moles of the elements at zero
temperature.The Unattainability of Absolute Zero
In Section 3.2, we showed that two reversible adiabats cannot cross. Since a reversible
adiabat corresponds to constant entropy, the curve representingT0 is a reversible
adiabat as well as an isotherm (curve of constant temperature). This is depicted in
Figure 3.12, in which the variableXrepresents an independent variable specifying
the state of the system, such as the volume or the magnetization. A reversible adiabat
gives the temperature as a function ofX. Since two reversible adiabats cannot inter-
sect, no other reversible adiabat can cross or meet theT0 isotherm. Therefore, no
reversible adiabatic process can reduce the temperature of the system to zero temper-
ature. Furthermore, since we found in Section 3.2 that irreversible adiabatic processes
lead to higher temperatures than a reversible adiabat, no adiabatic process, reversible
or irreversible, can lead to zero temperature.(^4) G. N. Lewis and M. Randall,Thermodynamics and the Free Energy of Chemical Substances, 1st ed.,
McGraw-Hill, New York, 1923, p. 448.