# Simple question on kinetic theory of matter

1. Oct 12, 2015

### iMatt

This came up whilst helping my kid with her GCSE physics so ought to be pretty straightforward. Here goes:

At his level the kinetic theory of matter is taught in a simple way and one "key point" which is stated time and time again is "the particles in a gas have more energy than the particles in a liquid which have more energy than the particles in a solid". Whist it is easy to see how this must be the case for the three states of the same substance it is not clear to me how it necessarily holds true when comparing different substances. For instance at room temperature one substance might be a solid and another might be liquid - does this "rule" always hold here? Or I might start with two equal masses of different solids at the same temperature then apply the same heat energy to both until one with lower melting point becomes liquid. Do the liquid particles have more energy than the particles of the substance that remains solid? If so this difference in energy must presumably have existed when both were still solid.

I don't know if the answer is tied in with considerations of different heat capacities for instance - I don't even know if the heat capacity and melting point of a substance are directly linked - but if I start listing all the things I don't know which might be relevant this email would get very long!

Hope someone can shed some light.

Thanks,

Matt

2. Oct 12, 2015

### PietKuip

In a gas, there is the Maxwell-Boltzmann distribution of velocities. Some of the molecules are really slow. So it is not correct to say that "the" (all ?) molecules in the gas have more energy than in other phases.

You are right to be suspicious. All this is quite complex. What is meant by the energy of a particle in solids or liquids? Kinetic energy? Some kind of potential energy? In a gas, kinetic energy is the only term that matters. In classical physics, it is the same for all molecules, whether it is helium or nitrogen.

3. Oct 13, 2015

### iMatt

Yes, I admit I kept away from gases in my examples because solids and liquids seemed to have more in common in his context. Having said that I suppose I had assumed the energy in question would be solely kinetic in nature but I have no basis for this other than the point arises in the GCSE section on the kinetic theory of matter

I might have hope my 25 yr old physics degree would be more help to me than it's proving to be - somehow it seems to be a question I don't remember asking myself before. Hopefully my rusty physics will at leat help me understand any suggested answers.

4. Oct 13, 2015

### nasu

That general statement is not true as it is given, without context.
The average energy per degree of freedom is the same, as long as the classical statistics can be applied.