Question

How do you prove average kinetic energy of molecules is directly proportional to the absolute temperature​

Answer 1

Answer:

Kinetic Molecular Theory states that gas particles are in constant motion and exhibit perfectly elastic collisions. The average kinetic energy of a collection of gas particles is directly proportional to absolute temperature only.

The following is the deduction of kinetic theory in terms of pressure:

p=mnv23

Where,

m is the mass of the gas molecule

n is the number of molecules per unit volume

v is the rms speed

So, n = NV

Where N is the number of molecules

Substituting for n we get,

pV=mNv23

mv22=E is the kinetic energy of the molecule

Therefore, pV=2NE3

From the ideal gas equation,

pV=μRT

Where μ=NNA

μRT=2NE3

NRTNA=2NE3

E=3kT/2

Where,

k=RNA

Therefore, it can be said that kinetic energy is proportional to temperature.