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I mean temperature is proportional to the average kinetic energy of the molecules (in an ideal gas, at least), and that depends on both their mass and the square root of their speed.

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    $\begingroup$ Thermometers work for liquids and solids as well as ideal gases ... $\endgroup$ May 4 '20 at 15:48
  • $\begingroup$ Nope! Square of the speed,not the square root. $\endgroup$
    – Bill N
    Aug 30 '20 at 23:52
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I wouldn't consider them that way, no.

As John Rennie mentions in the comments, thermometers work for solids, liquids and gasses, whereas the temperature being proportional to average kinetic energy is determined from gasses specifically.

Also, kinetic energy doesn't measure speed. Although it changes in proportion to the speed, it also depends directly on the mass. A thermometer doesn't differentiate between different masses of what it measures, so it cannot possibly be used to actually measure the speed of the particles.

To give another example, imagine you had a device that told you the kinetic energy of cars passing by you. This would not be a speed measurement device, because on it's own, the measurements from the device cannot tell you the speed. You would also need a way to know the mass of the car to determine it's speed, given the kinetic energy. The same would apply to gas molecules; telling you kinetic energy is not the same as telling you the speed, so calling a thermometer a speedometer for atoms is misleading.

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You cannot actually determine the concrete velocity of each particle, but by means of the Maxwell-Boltzmann distribution for the velocity vector:

$$f (v) = \left( \frac{m}{2 \pi kT} \right) ^{2/3} \exp \left(-m \frac{v^2}{2kT} \right)$$

It is possible to compute the mean velocity as:

$$\langle v\rangle= \int \mathrm dv \cdot f(v) v $$

And you end up having an expression which depends only on known constants and the temperature, so you can isolate the temperature from your equation.

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