0.13 Physical properties of gases  (Page 4/8)

Imagine that you are given a cup of water and asked to describe it as "hot" or "cold." Even without a calibrated thermometer, the experiment is simple: you put your finger in it. Only a qualitative question was asked, so there is no need for a quantitative measurement of "how hot" or "how cold" the water is. The experiment is only slightly more involved if you are given two cups of water and asked which one is hotter or colder. All we would have to do is put one finger in each cup and directly compare the differences in sensation. You still do not need a calibrated thermometer or even a temperature scale at all.

Finally, imagine that you are given a cup of water each day for a week and are asked to determine which day's cup contained the hottest or coldest water. Since you can no longer trust your sensory memory from day to day, you have no choice but to define a temperature scale. To do this, we make a physical measurement on the water by bringing it into contact with something else whose physical properties depend on the "hotness" of the water in some unspecified way. For example, the volume of mercury in a glass tube expands when placed in hot water, certain strips of metal expand or contract when heated, some liquid crystals change color when heated, and so on. We assume that this physical property will have the same value when it is placed in contact with two objects which have the same “hotness,” or temperature. This allows us to make comparisons in a quantitative way, which defines the temperature measurement. Keep in mind that, when we use a thermometer to measure how “hot” or “cold” and object is, we are actually measuring a physical property which varies with how hot or cold the object is.

For simplicity, we illustrate with a mercury-filled glass tube thermometer. We observe quite easily that when the tube is inserted in water we consider "hot," the volume of mercury is larger than when we insert the tube in water that we consider "cold." Therefore, the volume of mercury is a measure of how hot something is. Furthermore, we observe that, when two very different objects appear to have the same "hotness," they also give the same volume of mercury in the glass tube. This allows us to make quantitative comparisons of "hotness" or temperature based on the volume of mercury in a tube.

All that remains is to make up some numbers that define the scale for the temperature, and we can literally do this in any way that we please. This arbitrariness is what allows us to have two different but perfectly acceptable temperature scales, such as Fahrenheit and Centigrade. The latter scale simply assigns zero to be the temperature at which water freezes at atmospheric pressure. We then insert our mercury thermometer into freezing water, and mark the level of the mercury as "0". Another point on the Centigrade scale assigns 100 to be the boiling point of water at atmospheric pressure. We insert our mercury thermometer into boiling water and mark the level of mercury as "100." Finally, we just mark off in increments of 1/100 of the distance between the "0" and the "100" marks, and we have a working thermometer. Given the arbitrariness of this way of measuring temperature, it is not all obvious what physical property we are measuring, and as such it would be remarkable to find a quantitative relationship between temperature and any other physical property.