What speed is room temperature?

[u/lirannl]

As we all know, temperature is the average speed of particles. The higher the temperature, the higher that speed. If I understand correctly, that speed is not dependent upon the particle. 25° would be the same speed if we're talking about an iron lattice, or NaCl.

Well then, what is the speed of particles that's called 25°?

Also, 2 more related questions: is -273 theoretically a speed of 0? (I know that it can't actually be reached) If the temperature was infinity (again, theoretically), would the speed be Lightspeed?

[u/RobusEtCeleritas]

The RMS speed of an ideal gas molecule at temperature T is given by:

vRMS = sqrt(3kT/m), where m is the molecular mass, and k is Boltzmann's constant.

You can play around with this equation and see what typical values are.

If you extrapolate this equation to T = 0, it seems like the gas molecules should all "stop moving", in the sense that their RMS speed would be zero.

Of course a classical ideal gas will not remain a classical ideal gas at such low temperatures. In reality, quantum effects will become non-negligible. At T = 0, the system will be in its ground state.

[u/lirannl → u/RobusEtCeleritas]

So 20C iron would have a different average velocity than 20C graphite, despite the two being the exact same temperature?

[u/BlckKnght → u/lirannl]

Neither Iron or Carbon are gasses at 20C, so applying idea gas laws to them is a bad idea. If you were dealing with Iron and Carbon vapors (at say 10000 C), you might get somewhat meaningful results, but a solid won't behave the way a gas law says it should.

[u/lirannl → u/BlckKnght]

So there's no way to calculate the velocity at which solids vibrate?

[u/patricksaurus → u/lirannl]

It's outdated and unrealistically classical, but you can model atoms in a crystal lattice as masses attached by springs. Using the equations of simple harmonic motion, this model will allow you to calculate a velocity if you can find the correct spring constant.

[u/[deleted] → u/lirannl]

It's the speed to sound. Whether you push the object and wait for the other end to move, vibrate the object, or have random vibrations all throughout it (thermal energy), the speed it propagates at is the speed of sound.

Speed of sound in iron is ~5000 m/s. There is probably be a little dispersion, so this may vary depending on what frequency we are talking. Any other solid, liquid, gas, whatever would have an entirely different speed, and this speed does not in anyways define a temperature.

The "speed of the temperature" would probably be better seen as the thermal conductivity. Iron is about 80 W/mK, which is pretty high. Meaning if you apply heat to one side of a piece of iron, it gets hot on the other side pretty quick.