Page 27 - Physical Chemistry

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Having armed ourselves with a thermometer, we can now find the temperature of
Chapter 1
Thermodynamics any system B. To do so, we put system B in contact with the thermometer, wait until
thermal equilibrium is achieved, and then read the thermometer’s temperature from
the graduated scale. Since B is in thermal equilibrium with the thermometer, B’s tem-
perature equals that of the thermometer.
Note the arbitrary way we defined our scale. This scale depends on the expansion
properties of a particular substance, liquid mercury. If we had chosen ethanol instead
of mercury as the thermometric fluid, temperatures on the ethanol scale would differ
slightly from those on the mercury scale. Moreover, there is at this point no reason,
apart from simplicity, for choosing a linear relation between temperature and mercury
2
volume. We could just as well have chosen u to vary as aV b. Temperature is a fun-
r
damental concept of thermodynamics, and one naturally feels that it should be formu-
lated less arbitrarily. Some of the arbitrariness will be removed in Sec. 1.5, where the
ideal-gas temperature scale is defined. Finally, in Sec. 3.6 we shall define the most
fundamental temperature scale, the thermodynamic scale. The mercury centigrade
scale defined in this section is not in current scientific use, but we shall use it until we
define a better scale in Sec. 1.5.
Let systems A and B have the same temperature (u u ), and let systems B and
A
B
C have different temperatures (u u ). Suppose we set up a second temperature
B
C
scale using a different fluid for our thermometer and assigning temperature values in
a different manner. Although the numerical values of the temperatures of systems A,
B, and C on the second scale will differ from those on the first temperature scale, it
follows from the zeroth law that on the second scale systems A and B will still have
the same temperature, and systems B and C will have different temperatures. Thus, al-
though numerical values on any temperature scale are arbitrary, the zeroth law assures
us that the temperature scale will fulfill its function of telling whether or not two sys-
tems are in thermal equilibrium.
Since virtually all physical properties change with temperature, properties other
than volume can be used to measure temperature. With a resistance thermometer, one
measures the electrical resistance of a metal wire. A thermistor (which is used in a dig-
ital fever thermometer) is based on the temperature-dependent electrical resistance of
a semiconducting metal oxide. A thermocouple involves the temperature dependence
of the electric potential difference between two different metals in contact (Fig. 13.4).
Very high temperatures can be measured with an optical pyrometer, which examines
the light emitted by a hot solid. The intensity and frequency distribution of this light
depend on the temperature (Fig. 17.1b), and this allows the solid’s temperature to be
found (see Quinn, chap. 7; references with the author’s name italicized are listed in the
Bibliography).
Temperature is an abstract property that is not measured directly. Instead, we mea-
sure some other property (for example, volume, electrical resistance, emitted radia-
tion) whose value depends on temperature and (using the definition of the temperature
scale and calibration of the measured property to that scale) we deduce a temperature
value from the measured property.
Thermodynamics is a macroscopic science and does not explain the molecular
meaning of temperature. We shall see in Sec. 14.3 that increasing temperature corre-
sponds to increasing average molecular kinetic energy, provided the temperature scale
is chosen to give higher temperatures to hotter states.
The concept of temperature does not apply to a single atom, and the minimum-size
system for which a temperature can be assigned is not clear. A statistical-mechanical
calculation on a very simple model system indicated that temperature might not be a
meaningful concept for some nanoscopic systems [M. Hartmann, Contemporary
Physics, 47, 89 (2006); X. Wang et al., Am. J. Phys., 75, 431 (2007)].