The Ideal-Gas Temperature Scale 498
19.2 The Ideal-Gas 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 ideal-gas 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 triple-point 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 ptri. 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 ptri 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 ptri, 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 ideal-gas 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 constant-volume gas thermometer. The pressure gauge used in this thermometer consists of a closed-tube 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 ideal-gas temperature.
Table 19.1 lists some examples of temperatures of diverse bodies.
The ideal-gas thermometer plays a primary role in the measurement of temperature because, as we will see in Chapter 21, the ideal-gas 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 ideal-gas 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 ideal-gas thermometer is somewhat in convenient and is often replaced by mercury-bulb thermometers, bimetallic strips, electrical-resistance thermometers, or thermocouples. These must be calibrated in terms of the ideal-gas 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 triple-point 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.)
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.