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scale
(capital theta). Temperature ratios on the thermodynamic scale are thus Section 3.7
defined by What Is Entropy?
™ C q C (3.44)
™ H q H
Equation (3.44) fixes only the ratio
/
. We complete the definition of the
scale
C H
by choosing the temperature of the triple point of water as
273.16°.
tr
To measure the thermodynamic temperature
of an arbitrary body, we use it as
one of the heat reservoirs in a Carnot cycle and use a body composed of water at its
triple point as the second reservoir. We then put any system through a Carnot cycle
between these two reservoirs and measure the heat q exchanged with the reservoir
at
and the heat q exchanged with the reservoir at 273.16°. The thermodynamic
tr
temperature
is then calculated from (3.44) as
0q0
™ 273.16° (3.45)
0q 0
tr
Since the heat ratio in (3.45) is independent of the nature of the system put through the
Carnot cycle, the
scale does not depend on the properties of any kind of substance.
How is the thermodynamic scale
related to the ideal-gas scale T? We proved in
Sec. 3.2 that, on the ideal-gas temperature scale, T /T q /q for any system that
C H C H
undergoes a Carnot cycle; see Eq. (3.16). Moreover, we chose the ideal-gas temperature
at the water triple point as 273.16 K. Hence for a Carnot cycle between an arbitrary tem-
perature T and the triple-point temperature, we have

0q0
T 273.16 K (3.46)
0q 0
tr
where q is the heat exchanged with the reservoir at T. Comparison of (3.45) and (3.46)
shows that the ideal-gas temperature scale and the thermodynamic temperature scale
are numerically identical. We will henceforth use the same symbol T for each scale.
The thermodynamic scale is the fundamental scale of science, but as a matter of prac-
tical convenience, extrapolated measurements on gases, rather than Carnot-cycle mea-
surements, are used to measure temperatures accurately.

3.7 WHAT IS ENTROPY?

Each of the first three laws of thermodynamics leads to the existence of a state func-
tion. The zeroth law leads to temperature. The first law leads to internal energy. The
second law leads to entropy. It is not the business of thermodynamics, which is a
macroscopic science, to explain the microscopic nature of these state functions.
Thermodynamics need only tell us how to measure T, U, and S. Nevertheless it is
nice to have a molecular picture of the macroscopic thermodynamic state functions.
Temperature is readily interpreted as some sort of measure of the average molec-
ular energy. Internal energy is interpreted as the total molecular energy. Although we
have shown how S can be calculated for various processes, the reader may feel frus-
trated at not having any clear picture of the physical nature of entropy. Although en-
tropy is not as easy a concept to grasp as temperature or internal energy, we can get
some understanding of its physical nature.

Molecular Interpretation of Entropy
We saw in Sec. 3.5 that the entropy S of an isolated system is maximized at equilib-
rium. We therefore now ask: What else is maximized at equilibrium? In other words,