# Temperature & kinetic energy of particles in solid vs gas

Consider the internal energy of a gas and solid (different materials) both at the same temperature, which material has the larger potential energy and why? Do they also both have the same kinetic energy? Finally is the definition of temperature as the average kinetic energy of the particles only applicable to ideal gases

Drakkith
Staff Emeritus
Do they also both have the same kinetic energy?

I don't think so. I believe most of their energy is stored in the vibrational, rotational, and translational modes of the molecules.

The potential energy between the molecules tells us about the force of attraction between them. Kinetic energy, on the other hand, tells us how freely the molecules move. For solids, the potential energy dominates and the kinetic energy doesn't change too much with temperature. In case of gases, most of their energy is kinetic ( ideal gases are assumed to have zero potential energy). As for the relation between KE and temperature, that is derived for ideal gases. I expect real gases deviate from this relation (though i don't know the exact relation they'll follow)

edguy99
Gold Member
Most of the kinetic energy for gases is stored in the movement of molecules through space. This is used to model the temperature (i.e. the ideal gas law where collisions are ignored). For liquids, using the vibrational kinetic energy between molecules models the temperature pretty well (where molecules are not fixed to a particular location, only bonded to other molecules that are also vibrating and rotating). For solids, using the vibrational kinetic energy around a fixed grid works well (all molecules are vibrating as if bonded to a point on a fixed grid). No model is perfect, but in the words of George Box, one of the great statistical minds of the 20th century:

Now it would be very remarkable if any system existing in the real world could be exactly represented by any simple model. However, cunningly chosen parsimonious models often do provide remarkably useful approximations. For example, the law PV = RT relating pressure P, volume V and temperature T of an “ideal” gas via a constant R is not exactly true for any real gas, but it frequently provides a useful approximation and furthermore its structure is informative since it springs from a physical view of the behavior of gas molecules.

For such a model there is no need to ask the question “Is the model true?”. If “truth” is to be the “whole truth” the answer must be “No”. The only question of interest is “Is the model illuminating and useful?”.

Finally is the definition of temperature as the average kinetic energy of the particles only applicable to ideal gases
Experiments with gases leads to the relationship PV = Const x T
Kinetic theory models gases as a collection of particles with only translational KE (no rotational or vibrational KE) and leads to a relationship
PV = const x (average KE of particles)
These 2 equations from experimental and theoretical analysis indicate that temperature T is a measure of the average translational KE of molocules.