12.2

The Kelvin Temperature Scale

Although the Celsius and Fahrenheit scales are widely used, the Kelvin temperature scale has greater scientific significance. It was introduced by the Scottish physicist William Thompson (Lord Kelvin, 1824–1907), and in his honor each degree on the scale is called a kelvin (K). By international agreement, the symbol K is not written with a degree sign (°), nor is the word “degrees” used when quoting temperatures. For example, a temperature of 300 K (not 300 °K) is read as “three hundred kelvins,” not “three hundred degrees kelvin.” The kelvin is the SI base unit for temperature.
Figure 12-2 compares the Kelvin and Celsius scales. The size of one kelvin is identical to that of one Celsius degree because there are one hundred divisions between the ice and steam points on both scales. As we will discuss shortly, experiments have shown that there exists a lowest possible temperature, below which no substance can be cooled. This lowest temperature is defined to be the zero point on the Kelvin scale and is referred to as absolute zero.

Figure 12-2 A comparison of the Kelvin and Celsius temperature scales.

The ice point (0 °C) occurs at 273.15 K on the Kelvin scale. Thus, the Kelvin temperature T and the Celsius temperature Tc are related by

| (12.1)

The number 273.15 in Equation 12.1 is an experimental result, obtained in studies that utilize a gas-based thermometer. When a gas confined to a fixed volume is heated, its pressure increases. Conversely, when the gas is cooled, its pressure decreases. For example, the air pressure in automobile tires can rise by as much as 20% after the car has been driven and the tires have become warm. The change in gas pressure with temperature is the basis for the constant-volume gas thermometer.
A constant-volume gas thermometer consists of a gas-filled bulb to which a pressure gauge is attached, as in Figure 12-3. The gas is often hydrogen or helium at a low density, and the pressure gauge can be a U-tube manometer filled with mercury. The bulb is placed in thermal contact with the substance whose temperature is being measured. The volume of the gas is held constant by raising or lowering the right column of the U-tube manometer in order to keep the mercury level in the left column at the same reference level. The absolute pressure of the gas is proportional to the height h of the mercury on the right. As the temperature changes, the pressure changes and can be used to indicate the temperature, once the constant-volume gas thermometer has been calibrated.

Figure 12-3 A constant-volume gas thermometer.

Suppose the absolute pressure of the gas in Figure 12-3 is measured at different temperatures. If the results are plotted on a pressure-versus-temperature graph, a straight line is obtained, as in Figure 12-4. If the straight line is extended or extrapolated to lower and lower temperatures, the line crosses the temperature axis at −273.15 °C. In reality, no gas can be cooled to this temperature, because all gases liquify before reaching it. However, helium and hydrogen liquify at such low temperatures that they are often used in the thermometer. This kind of graph can be obtained for different amounts and types of low-density gases. In all cases, a straight line is found that extrapolates back to −273.15° C on the temperature axis, which suggests that the value of −273.15° C has fundamental significance. The significance of this number is that it is the absolute zero point for temperature measurement. The phrase “absolute zero” means that temperatures lower than −273.15 °C cannot be reached by continually cooling a gas or any other substance. If lower temperatures could be reached, then further extrapolation of the straight line in Figure 12-4 would suggest that negative absolute gas pressures could exist. Such a situation would be impossible, because a negative absolute gas pressure has no meaning. Thus, the Kelvin scale is chosen so that its zero temperature point is the lowest temperature attainable.

Figure 12-4 A plot of absolute pressure versus temperature for a low-density gas at constant volume. The graph is a straight line and, when extrapolated (dashed line), crosses the temperature axis at −273.15 °C.

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.