Ten-thousandths of a degree from a bottle. Drawing, description

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Ten-thousandths of a degree from a bottle. Children's Science Lab

Children's Science Lab

Modern scientific equipment is extremely sensitive and works with tremendous precision. Masses of separate elementary particles, sizes of atoms and molecules are measured. Thermometers are capable of capturing temperature differences of a thousandth of a degree, and interferometers are capable of detecting displacements of the order of the diameter of an atom. All of these highly precise instruments are extremely complex and are based on the latest technical innovations.

But you can build an extremely sensitive thermometer from the simplest items: a glass bottle, an empty ballpoint pen, a ruler, and a piece of plasticine.

(click to enlarge)

Cut off the writing knot from the rod, run a drop of ink into the tube and insert it into the neck of the bottle, tightly sticking it with plasticine. Lay the bottle on its side to eliminate the effect of gravity on the vial. Place a ruler with millimeter divisions next to it. The device is ready.

For some time, the ink bubble will move to the right or to the left due to the fact that the temperature of the container changes, coming into thermal equilibrium with air. Let's wait for it to stop, and notice at which division it ended up. Now let's touch the wall of the bottle with our finger. The air in it will heat up, expand, and the bubble in the tube will move a few millimeters. Let's evaluate the accuracy of our device.

The dependence of the change in gas volume on temperature is determined by the formula, which was derived by the French physicist and chemist Joseph Louis Gay-Lussac in 1802:

V_t=V(1 + B_tdt),

where V is the initial volume of gas; V_t - the volume that it began to occupy when the temperatures changed by dt; B_t\u1d 273/XNUMX deg^-1 - coefficient of volume expansion of gas. It shows that the volume of a certain mass of gas when heated increases by 1/273 of that volume V₀, which this mass occupied at 0°C. But, since we are conducting a purely qualitative experiment, to reduce the volume of gas V to the value V₀ doesn't make sense.

Ten thousandths of a degree from a bottle
The graph of the Gay-Lussac equation is a straight line in coordinates: temperature T - volume V. As the temperature decreases, the volume of gas decreases and becomes equal to zero at a temperature of -273,15 ° C. In reality, this is impossible - gas molecules have a volume, which, of course, cannot go anywhere.

From the Gay-Lussac formula it follows that

dt = (V_t -V)/VB_t = dV/VB_t.

Glass bottle volume V₀ = 750 cm³ = 7,5 * 10³ mm³, tube inner diameter D = 1,5 mm, radius r = 0,7 mm, hole area s ~ 1 mm². We will assume that the position of the bubble can be determined with an accuracy of 1 mm and, therefore, a change in the volume of air in the container by 1 mm can be detected.³. Substituting these values into the above formula, we get dt = 1*273/7,5*10³ = 3,64 * 10^-4 degrees.

This is very high accuracy. But to use such a device in practice, unfortunately, is problematic. It will respond with no less sensitivity to changes in atmospheric pressure, cooling by drafts and other extraneous influences.

Author: S.Trankovsky

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