Question

What is kinetic energy of gas? How can it be derived?

Answer 1

Kinetic energy of a gas is the kinetic energy possessed by the molecules of the gas, at a given temperature. We know that,

PV = 1/3 mNu²

where, m = mass of gas molecule

N = Total number of molecules

u = root mean square speed of the molecules

P= Pressure of the gas

V = volume of the gas.

P = 1/3 (N/V) mu².

For one mole of a gas, N = N_A (Avogadro's number)

PV = 1/3 N_Amu².

Also, for one mole of gas PV = RT

1/3 N_Amu² = RT

Multiply and divide the LHS by 2 we get,

(1/2)(2/3) N_Amu² = RT

1/2 N_Amu² = (3/2) RT

mu² = Average Kinetic energy of the molecule

K.E = 3/2 RT

or K.E = (3/2) (R/N_A) T

K.E = 3/2 kT

where k = Boltzmann's constant.