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# The Air Thermometer

Determination of the Coefficient of Increase of Pressure of a Gas at constant Volume per Degree of Temperature.

The air is contained in a closed flask or bulb, which can be heated to any required temperature. From this a tube, after being bent twice at right angles, passes vertically downwards to a reservoir of mercury, into one end of which a plunger is fitted. A second and longer vertical tube is also screwed into this reservoir. On the tube connecting the bulb with the reservoir is a mark, which should be as near the bulb as it can conveniently be.

By means of the plunger the level of the mercury in this tube is adjusted until it coincides with the mark, the bulb being kept at 0°C by immersion in melting ice. The mercury at the same time moves in the other tube, and the difference of level of the two columns is measured by means of the kathetometer or of scales placed behind the tubes.

Let this difference be 5.62 cm., and, suppose the height of the barometer to be 75.38 cm., then the pressure on the enclosed gas is that due to a column of mercury 81 cm. in height.

It is of the greatest importance that the air in the bulb should be free from moisture. The bulb must, therefore, have been thoroughly dried and filled with dry air by the use of the three-way cock, drying tubes, and air-pump, as already described, (§16). In Jolly's air-thermometer the three-way cock is permanently attached to the tube which connects the bulb with the reservoir.

The bulb is next immersed in a vessel of water which is made to boil, or, better still, in the steam from boiling water. The mercury is thus forced down the tube connected with the bulb, but by means of the plunger it is forced back until it is level again with the mark. At the same time it rises considerably in the other tube. When the water boils and the conditions have become steady, the difference of level in the two tubes is again noted. Suppose we find it to be 34.92 cm., and that the barometer has remained unchanged.

The air is now under a pressure due to 110.3 cm. of mercury, its volume remaining the same. The increase of pressure, therefore, is that due to 29.3 cm., and the coefficient of increase per degree centigrade is

29.3/(81x100) = 0.00362.

In this case it is important that the lower temperature should be 0°C, for to determine the coefficient we have to divide by the pressure at 0°C., and the difference between this and the pressure at the temperature of the room, say 15°, is too great to be neglected, as in the case of a solid or liquid.

If greater accuracy be required, allowance must be made for the expansion of the glass envelope, and for that portion of the air in the connecting tube which is not at the temperature of the bath.

The same apparatus can be used to determine the coefficient of increase of volume at constant pressure per degree of temperature.

In this case make the first observation as before, noting at the same time the height at which the mercury stands in the marked tube. Now heat the bulb. The air will expand and drive the mercury down the one tube and up the other, thus increasing at the same time the volume of the air and the pressure to which it is subject. By withdrawing the plunger the mercury is allowed to sink in both tubes. It must, however, sink faster in the one open to the external air, and after a time a condition will be reached in which the difference between the levels in the two is the same as it was originally. The air in the bulb is under the same pressure as previously, but its temperature has been raised to 100°C. and its volume altered. Observe the level of the mercury in the tube connected with the bulb. If the bore of this tube be known, the change of level will give the increase of volume; hence, knowing the original volume, the coefficient of expansion per degree of temperature can be found.

Owing to the large amount of expansion produced in a gas by a rise of temperature of 100°C, a tube of large bore is required.

The method, however, as here described will not lead to very accurate results, for it is almost impossible to insure that the air in the bulb and that in the tube should be all at the same high temperature. In the first method, on the other hand, the portion of tube occupied by air can be made very small, so as easily to be jacketed along with the bulb and kept at an uniform high temperature.

The method is open to the objection that the air in contact with the mercury, and therefore the mercury itself, is at a different temperature in the two parts of the experiment. The density of the mercury, therefore, is different and the increment of pressure is not strictly proportional to the difference of level. This error will be but small.

We have described the experiment as if air was the gas experimented with. Any other gas which does not attack the mercury may be used.

Experiment. - Determine for the given gas the coefficient of the increase of pressure per degree of temperature at constant volume.

Enter results thus:

```Difference of level of mercury at 0°C: 5.62 cm
Difference of level of mercury at 100°C: 34.92 cm
Barometer: 75.38 cm
Coefficient of expansion: 0.00362
```

Last Update: 2011-03-27