CHAPTER 2 SYSTEMS AND THEIR PROPERTIES
2.3 SOMEBASICPROPERTIES ANDTHEIRMEASUREMENT 40
forces at a point within a solid are described by the nine components of a stress tensor. The
statement that a solidhasoris ata certain pressure means that this is the hydrostatic pressure
exerted on the solid’s exterior surface. Thus, a solid immersed in a uniform isotropic fluid
of pressurepis at pressurep; if the fluid pressure is constant over time, the solid is at
constant pressure.
2.3.5 Temperature
Temperature scales
Temperature and thermometry are of fundamental importance in thermodynamics. Unlike
the other physical quantities discussed in this chapter, temperature does not have a single
unique definition. The chosen definition, whatever it may be, requires atemperature scale
described by an operational method of measuring temperature values. For the scale to be
useful, the values should increase monotonically with the increase of what we experience
physiologically as the degree of “hotness.” We can define a satisfactory scale with any
measuring method that satisfies this requirement. The values on a particular temperature
scale correspond to a particular physical quantity and a particular temperature unit.
For example, suppose you construct a simple liquid-in-glass thermometer with equally
spaced marks along the stem and number the marks consecutively. To define a temperature
scale and a temperature unit, you could place the thermometer in thermal contact with a
body whose temperature is to be measured, wait until the indicating liquid reaches a stable
position, and read the meniscus position by linear interpolation between two marks.^5
Thermometry is based on the principle that the temperatures of different bodies may
be compared with a thermometer. For example, if you find by separate measurements with
your thermometer that two bodies give the same reading, you know that within experimental
error both have the same temperature. The significance of two bodies having the same
temperature (on any scale) is that if they are placed in thermal contact with one another,
they will prove to be in thermal equilibrium with one another as evidenced by the absence
of any changes in their properties. This principle is sometimes called thezeroth law of
thermodynamics, and was first stated as follows by J. C. Maxwell (1872): “Bodies whose
temperatures are equal to that of the same body have themselves equal temperatures.”^6
Two particular temperature scales are used extensively. Theideal-gas temperature
scaleis defined by gas thermometry measurements, as described on page 42. Thether-
modynamic temperature scaleis defined by the behavior of a theoretical Carnot engine,
as explained in Sec.4.3.4. These temperature scales correspond to the physical quanti-
ties called ideal-gas temperature and thermodynamic temperature, respectively. Although
the two scales have different definitions, the two temperatures turn out (Sec.4.3.4) to be
proportional to one another. Their values become identical when the same unit of temper-
ature is used for both. Thus, thekelvinis defined by specifying that a system containing
the solid, liquid, and gaseous phases of H 2 O coexisting at equilibrium with one another
(the triple point of water) has a thermodynamic temperature of exactly273:16kelvins. We
(^5) Of course, placing the thermometer and body in thermal contact may affect the body’s temperature. The
measured temperature is that of the bodyafterthermal equilibrium is achieved.
(^6) Turner (Ref. [ 160 ]) argues that the “zeroth law” is a consequence of the first and second laws and therefore is
not a separate assumption in the axiomatic framework of thermodynamics. The term “law” for this principle is
also questioned by Redlich (Ref. [ 142 ]).