19.2 The IdealGas Temperature Scale
To use Eq. (1) for the definition of temperature, we
take a fixed amount of some gas, say, helium, and place it in an airtight,
nonexpanding container, say, a Pyrex glass bulb. The amount of gas should
be small, so the density and pressure are low, and the gas behaves like
an ideal gas. According to Eq. (1), the pressure of an ideal gas kept
in such a constant volume is directly proportional to the temperature.
Thus, a simple measurement of pressure gives us the temperature.
To calibrate the scale of this idealgas thermometer,
we must choose a standard reference temperature. The standard adopted
in the SI system of units is the temperature of the triple
point of water, that is, the temperature at which water, ice, and
water vapor coexist when placed in a closed vessel. Figure
19.3 shows a triplepoint cell used to achieve the standard temperature.
This standard temperature has been assigned the value 273.16 kelvin, or
273.16 K. If the bulb of the gas thermometer is placed in thermal contact
with this cell so that it attains a temperature of 273.16 K, it will read
some pressure p_{tri}. If the bulb
is then placed in thermal contact with some body at an unknown temperature
T, it will read a pressure p which is greater or smaller
than p_{tri} by some factor. The
unknown temperature T is then greater or smaller than 273.16 K
by this same factor; for instance, if the pressure p is half as
large as p_{tri}, then T =
½ X 273.16 K.
In general, the temperature T may be expressed
as
This equation calibrates our thermometer. The temperature
scale defined in this way is called the idealgas
temperature scale.
When connecting a pressure gauge to the bulb of gas,
we must take special precautions to ensure that the operation of the pressure
gauge does not alter the volume available to the gas. Figure
19.4 shows a device that will serve our purposes; this device is called
a constantvolume gas thermometer. The pressure gauge used in this
thermometer consists of a closedtube manometer; one branch of the manometer
is connected to the bulb of gas, and the other branch consists of a closed,
evacuated tube. The difference h in the heights of the levels of
mercury in these two branches is proportional to the pressure of the gas.
The manometer is also connected to a mercury reservoir. During the operation
of the thermometer, this reservoir must be raised or lowered so that the
level of mercury in the left branch of the manometer tube always remains
at a constant height; this keeps the gas in the bulb at a constant volume.
The bulb of this thermometer may be put in thermal contact with any body
whose temperature we wish to measure, and the pressure registered by the
manometer then gives us the idealgas temperature.
Table 19.1 lists some examples of temperatures of diverse
bodies.
The idealgas thermometer plays a primary role in the
measurement of temperature because, as we will see in Chapter 21, the
idealgas temperature scale coincides with the Kelvin temperature scale,
also called the absolute thermodynamic temperature scale, which is the
fundamental temperature scale for the study of thermodynamic processes.
The name kelvin, which we introduced for the unit of temperature
in Section 19.1, anticipates this coincidence of the idealgas temperature
scale and the Kelvin scale. To simplify the terminology, we will hereafter
use the single name Kelvin scale for both of these scales.
For practical applications, the idealgas thermometer
is somewhat in convenient and is often replaced by mercurybulb thermometers,
bimetallic strips, electricalresistance thermometers, or thermocouples.
These must be calibrated in terms of the idealgas thermometer so they,
too, will read Kelvin temperature. We will deal with some details of these
secondary thermometers in the next chapter.
Although the Kelvin temperature scale is the only scale
of fundamental significance, several other temperature scales are in practical
use. The Celsius scale (formerly known as
the centigrade scale) is shifted by 273.15 degrees relative
to the Kelvin scale,
Note that on the Celsius scale, absolute zero is at 
273.15°C. The triple point of water is then at 0.01°C, and the boiling
point at 100°C. The freezing point of water, at atmospheric pressure,
is at 0°C (The slight difference between the temperatures of the freezing
point and the triple point is due to the difference in the pressure of
the water. Normal freezing occurs at normal atmospheric pressure, whereas
the upper portion of the triplepoint cell is evacuated and contains only
a small amount of water vapor of very low pressure. In water, a lowering
of the pressure causes a rising of the freezing point.)
The Fahrenheit scale is
shifted relative to the Celsius scale and, furthermore, uses degrees of
smaller size, each degree Fahrenheit corresponding to 5/9 degree Celsius:
On this scale, the freezing point of water is at 32°F
and the boiling point at 212°F. Figure
19.5 can be used for rough conversions between the Fahrenheit and Celsius
scales.

