show that the Average translational kinetic energy of the molecules of a gas is directly proportional to absolute temperature.

**Proof**

According to the kinetic equation of pressure of a gas:

But r = density of gas

r = density of gas = mass of gas / volume of gas

r = density of gas = mN / V

Putting the value of density (r)

But PV = nRT

putting the value of PV, we get,

Since

number of mole (n) = molecules/Avogadro’s number

number of mole (n) = N/NA

Therefore,

But NA R = Boltzman’s constant (K), thus

Multiplying both sides by 1/2

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