If I understood correctly, temperature is simply the average kinetic energy of the particles in a system. Temperature differs from heat in that heat is the total energy in a system, the kinetic + the potential energy.

 

What I don't get is, is temperature dependent on the number of moving particles in the system?

 

Let's say there are 2 isolated systems and in one system there there are 10 moving particles and in the second system there are only 3 moving particles . If in both systems the particles have the same kinetic energy, will both systems have the same temperature regardless of the number of particles?

as temperature is an average of the kinetic energy per particle, yes, they will have the same temperature. it is independant of the number of them, although as you get down below a few thousand particles it all becomes rather meaningless.

 

ajb, i think your wording about thermodynamics not applying is a bit misleading, thermodynamics still applies, but manifests much differently than at macroscopic scales.

 

ajb, i think your wording about thermodynamics not applying is a bit misleading, thermodynamics still applies, but manifests much differently than at macroscopic scales.

 

Yes indeed. (I have withdrawn the statement almost as soon as I posted it!)

 

(What we really mean is that "statistical mechanics becomes thermodynamics" in the limit of the number of particles tends to infinity. )

as temperature is an average of the kinetic energy per particle, yes, they will have the same temperature. it is independant of the number of them, although as you get down below a few thousand particles it all becomes rather meaningless.

 

But why does it become meaningless below a few thousand particles?

simply because it is useless, there is no such thing as a defined solid/liquid/gas when you only have a few thousand atoms or so. and the changes in temperature due to interaction with the container walls can be huge(thousands of kelvin) and over incredibly short time scales(pico seconds) so any measurement you make may or may not accurately reflect the actual properties. it is far easier to switch to eV as a measure of energy in the system.