Potential Energy in Gases

when i was reading about the Kinetic theory, i came across a relation stating U = + + 1/2(dy/dt)^2+1/2ky^2 But when a gas molecule moves away from its mean position of vibration, why should it return back to its mean position... what applies that restoring force. In solids, this may be due to repulsion from neighboring molecules but inter-molecular distance in gas is very high and thus, this possibility is ruled out. But when a gas molecule moves away from its mean position of vibration, why should it return back to its mean position... what applies that restoring force. In solids, this may be due to repulsion from neighboring molecules but inter-molecular distance in gas is very high and thus, this possibility is ruled out. also while applying this formula for gases, v might be got from temperature, but how can we determine the w(omega), k (stiffness constant). also when we differentiate displacement y with respect to time t, we get the answer in terms of t as y varies non-linearly with y what 'average' value is chosen for t
- sanket singh (age 14)
patna, bihar, india

Your thoughts are right on track. The spring-like potential energy term is present in the thermal energy of solids. In gases the molecules are usually out of reach of each others forces. There's almost no thermal potential energy from their interactions, certainly much less than the equipartition energy value of the translational kinetic energy.


There are no appreciable restoring forces on a gas molecule as it moves about. The springiness of gases (as in inflated tires) doesn't come from interactions between molecules. It comes from the entropy of the molecules. The molecules in an expanded gas region have more states available to them.

Mike W.

(published on 04/29/2012)