Measuring Kelvin Temperature

Measuring Kelvin Temperature

To understand how to use the Kelvin temperature scale, we need to answer two questions:

1. If I know the temperature in degrees Centigrade, how do I find it in Kelvin?

2. If the Kelvin temperature does not depend on any material, how in the world do we measure it?

Answer to 1. T (K) = θ (^oC) + 273.15. This means the Kelvin temperature is equal to the Centigrade temperature plus 273.15. For example, 0 ^oC is 273.15 K, and 25 ^oC is 298.15 K.

Answer to 2. It looks, from the the previous answer, like we can just use a mercury thermometer, measure the Centigrade temperature, and then add 273.15 to find the Kelvin temperature. Does this not make it dependent on the material used in the therometer? Unfortunately, we have to say that the answer to question 1 is only an approximate method. Does an exact method exist?

It does. We shall only look at one such method here. This method involves two steps: (i) Make an ideal gas. (ii) Use the ideal gas to make a thermometer.

Since the ideal gas is purely imaginary, it does not depend on the property of any real material. However, if it is imaginary, how do we make a thermometer from it? The idea is as follows.

The main features of an ideal gas are: (i) there is no attraction between molecules, and (ii) the size of an atom is negligible. If we take a real gas like nitrogen, and allow it to expand, the molecules move further apart. Then attraction decreases, and size of the molecules becomes smaller compared to the average distance between molecules. So if we let a real gas expand more and more, it approaches an ideal gas.

An ideal gas obeys the gas law, which says that pressure is proportional to the Kelvin temperature. So we can use the pressure to measure the Kelvin temperature. The idea is to find the temperature, expand the gas, find the temperature again, and repeat this a few times.

We then plot a few points on a graph of temperature against pressure, and extrapolate the graph to zero pressure. At zero pressure, the gas becomes ideal, since the molecules are infinitely far apart. This also means that the volume is infinite. Although we can never actually produce this ideal gas, the graph allows us to deduce the ideal gas temperature by drawing a line through the points and extending it to find the temperature when pressure is zero.

The above procedure makes up the ideal gas thermometer. It is truly independent of the actual gas used. Experiments have shown that nitrogen, oxygen, hydrogen, helium all give different temperatures at normal pressure, but the same Kelvin temperature when extrapolated to zero pressure on the graph.

Finally, we should mention what the difference between the Centigrade and the Celsius scale is. Centigrade and Celsius scales are often used as if they are the same. In practice, they are usually quite close, so it is not a big problem. The exact relation is:

T (Kelvin) = θ (^oCelsius) + 273.15.

This is how the Celsius scale is defined. If we replace Celsius by Centigrade, then the formula becomes approximate, as in the answer to question 1 above. So the Celsius scale is calculated from the Kelvin scale and does not depend on material properties of thermometers. The Celsius scale is approximately equal to the Centigrade scale which does depend on material properties.

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