Consider the following usages of the word "theory."
However, is always a work in progress, and even theories change.
A traditionalist could argue that a gas molecule behaves like a superball when it collides with a wall, i.e. v1f= -v1i. Of course this fits with an elastic collision and relative velocities, but not necessarily with eqn 1.10.38 because the walls mass is infinite compared to the gas molecule. The awkwardness goes beyond this, because no real mechanism for both the walls and gas molecules being related to kT/2 is given. If you accept this author’s assertion, that massive walls pump a given energy onto the gas molecules, then the relationship is understood without the requirement of elastic collisions.
In fact, theories often integrate and generalize many hypotheses.
If for some reason you removed the starter unit and found some of the bottom outer coils were considerably larger that the uppers, someone has tried before to replace it, but wound the spool CLOCKWISE. This will make it hard to reassemble where you need to get the outer lower hook in the proper slot of the retainer plate AND at the same time this hook into the underside front recess of the lower main housing. You may have to try to reshape some of these coils using pliers. Then to assemble, (with the aid of a helper) the spring needs to go into the lower hole in the main housing, and the retainer plate brought up from the bottom so it allows the spring's hook to rest in the groove in the main housing, all the while you need to slide the retainer plate up AND the spring down so the spring's tail is secured out through the retainer's slot AND the housing. Insert and tighten the two lower bolts.
In fact, few theories fit our observations of the world perfectly.
Interestingly, the mean free path does not directly depend upon the gas molecule’s velocity, however in reality it does, because at a given pressure gas molecules with higher kinetic energy will tend to occupy a greater mean molecular volume, hence a lower number of molecules per unit volume (n). Furthermore eqn 1.10.37 remains an approximation as molecules have attractions at large distances and repulsion at short distances i.e. Lennard-Jones potential.
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Now imagine, when gaseous molecules do collide that heat is given off, hence such collisions are not perfectly elastic, yet energy is conserved. If inelastic collisions occur within a closed system, then the other gas molecules and/or the surrounding walls should absorb any collision derived heat that is given off. Accordingly, such heat would become part of the equilibrium state between molecular collisions and vibrations, along with the emission and absorption of thermal radiation.