Thermodynamics

The idea of temperature is well known to everyone, but the need to define it so that it can be used for measurements is far more complex than the simple concepts of "hot" and "cold." If a rod of metal is placed in an icewater bath and the length is measured, and then placed in a steam bath and the length again measured, it will be found that the rod has lengthened. This is an illustration of the fact that, in general, materials expand when heated, and contract when cooled (however, under some conditions rubber can do the opposite, while water is a very special case and is treated below). One could therefore use the length of a rod as a measure of temperature, but that would not be useful, since different materials expand different amounts for the same increase in temperature, so that everyone would need to have exactly the same type of rod to make certain that they obtained the same value of temperature under the same conditions.

However, it turns out that practically all gases, at sufficiently low pressures, expand in volume exactly the same amount with a given increase in temperature. This has given rise to the constant volume gas thermometer, which consists of a flask to hold the gas, attached to a system of glass and rubber tubes containing mercury. A small amount of any gas is introduced into the (otherwise empty) flask, and the top of the mercury in the glass column on the left is placed at some mark on the glass (by moving the right hand glass column up or down). The difference between the heights of the two mercury columns gives the difference between atmospheric pressure and the pressure of the gas in the flask. The gas pressure changes with a change in temperature of the flask, and can be used as a definition of the temperature by taking the temperature to be proportional to the pressure; the proportionality factor can be found in the following manner. If the temperature at the freezing point of water is assigned the value 0° and that at the boiling point is called 100°, the temperature scale is called the Celsius scale (formerly called Centigrade); if those points are taken at 32° and 212°, it is known as the Fahrenheit scale. The relationship between them can be found as follows. If the temperature in the Celsius scale is T(°C), and that in the Fahrenheit scale is T(°F), they are related by T(°F)=(9/5)T(°C)+32°. The importance of using the constant volume gas thermometer to define the temperature is that it gives the same value for the temperature no matter what gas is used (as long as the gas is used at a very low pressure), so that anyone at any laboratory would be able to find the same temperature under the same conditions. Of course, a variety of other types of thermometers are used in practice (mercury-in-glass, or the change in the electrical resistance of a wire, for example), but they all must be calibrated against a constant volume gas thermometer as the standard.