# From the pressure law to the Kelvin scale

The experimental graph of pressure against temperature is likely to be straight enough to justify asking whether the plotted points (the true results of the experiment) fit closely to an ideal simple law. This is what we would like to find because it makes our description of nature easy and simple. If some students have graphs that do not seem to suggest a straight line, then a 'picture gallery' of everybody's graph can be organized. That will enable the class to extract a general conclusion, as in a professional research team's work.

Then suggest each student should extend the line backwards to look for absolute zero. They can either draw new axes so the temperature scale can be extended backwards to about 300ºC below the ice point or pages of graph paper stuck to the original graph until the line cuts the temperature axis. It is also possible to calculate the position of absolute zero algebraically, using the slope of the line.

Get students to think on these lines:

What happens to the motion of the molecules when you cool the air? Think of cooling the air more and more... could you cool it until its molecules had no motion at all? Suppose there was such a temperature: somewhere far down on the scale of the thermometer at which molecules would have no motion at all. What would the pressure be like at that temperature? If we trust our picture of gas models we expect the pressure to fall to nothing.

Students should emerge with a clear idea that, judged by a mercury thermometer, gas pressure runs down an almost straight line as temperature falls. The straight line reaches zero pressure at a temperature somewhere between -250ºC and -300ºC (-273°C), called absolute zero. Tell them this process of extending the graph backwards beyond the reading is called extrapolation. It is a risky process because we do not know if the gas will continue to behave in the same way.

You could ask students to imagine an ideal gas and discover what the temperature would be at which that gas would collapse with no useful motion.

Say:

The absolute scale of temperature can be defined by shifting the zero from the ice point to this new zero and reckoning all temperatures from there. All we do is add 273 to all Celsius temperatures in order to create the temperature on this new Kelvin scale. The close agreements amongst many gases persuade us to redefine our temperature measurement for gas thermometers and then finally move to the Kelvin scale. The Kelvin scale has several advantages:

• If you keep the volume of a sample of gas constant, its pressure goes up in direct proportion to the Kelvin temperature. This is automatically true for an ideal gas; fortunately many gases have almost identical behaviour, except at very low temperatures.
• For standard thermometers, you can change from ordinary mercury thermometers, which are convenient, to a gas thermometer. This is a bulb and pressure gauge similar to the class experiment. Instead of using it to investigate a sample of air, turn the argument round and say:

'Henceforth we choose to measure temperatures on a scale that uses a gas thermometer with an ideal gas in it'.

• There is a very fruitful theory of heat engines, thermodynamics, which offers many remarkable predictions, all of which necessarily use the Kelvin scale. Without the idea of that scale, and without practical gas thermometers for measurements, the predictions of thermodynamics would be useless, just 'hot air'.

You will find that real gases give an almost straight line graph when their pressure is plotted against Kelvin temperature. The expansion of mercury happens, by a lucky chance, to give a fairly straight line when plotted against Kelvin temperature measured by a gas thermometer. That lucky chance makes it comfortable to use mercury thermometers for measuring ordinary temperatures in the laboratory. For higher temperatures, Bunsen flames, mercury thermometers are useless and in very cold weather the mercury freezes. The Kelvin scale extends from zero as high as you like, millions of degrees in nuclear fusion.

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