Any physical property that changes with temperature can be used as a thermometer. In practice, the most useful thermometers have a physical property that changes linearly with temperature. One of the most important scientific thermometers is the constant-volume gas thermometer shown in FIGURE 18.3a. This thermometer depends on the fact that the absolute pressure (not the gauge pressure) of a gas in a sealed container increases linearly as the temperature increases.

FIGURE 18.3 The pressure in a constant-volume gas thermometer extrapolates to zero at $T_0=-273\text{°}\text{C}$.

A gas thermometer is first calibrated by recording the pressure at two reference temperatures, such as the boiling and freezing points of water. These two points are plotted on a pressure-versus-temperature graph and a straight line is drawn through them. The gas bulb is then brought into contact with the system whose temperature is to be measured. The pressure is measured, then the corresponding temperature is read off the graph.

FIGURE 18.3b shows the pressure-temperature relationship for three different gases. Notice two important things about this graph.

1. There is a linear relationship between temperature and pressure.

2. All gases extrapolate to zero pressure at the same temperature: $T_0=-273.15\text{°}\text{C}$. No gas actually gets that cold without condensing, although helium comes very close, but it is surprising that you get the same zero-pressure temperature for any gas and any starting pressure.

The pressure in a gas is due to collisions of the molecules with each other and the walls of the container. A pressure of zero would mean that all motion, and thus all collisions, had ceased. If there were no atomic motion, the system’s thermal energy would be zero. The temperature at which all motion would cease, and at which $E_{\text{th}}=0$, is called absolute zero. Because temperature is related to thermal energy, absolute zero is the lowest temperature that has physical meaning. We see from the gas-thermometer data that $T_0=-273.15\text{°}\text{C.}$ In practice, this can almost always be rounded to $T_0=-273\text{°}\text{C.}$

It is useful to have a temperature scale with the zero point at absolute zero. Such a temperature scale is called an absolute temperature scale. Any system whose temperature is measured on an absolute scale will have $T>0$. The absolute temperature scale having the same unit size as the Celsius scale is called the Kelvin scale. It is the SI scale of temperature. The units of the Kelvin scale are kelvins, abbreviated as K. The conversion between the Celsius scale and the Kelvin scale is

On the Kelvin scale, absolute zero is 0 K, the freezing point of water is 273 K, and the boiling point of water is 373 K.