HEAT CAPACITY
For a monatomic ideal gas (one in which there is no rotational or vibrational energies), the above theory predicts that the amount of energy necessary to heat the gas (what we call the heat capacity) would be:
where Q is the energy to raise temperature of an amount of material by ?T.
Since KE = (3/2)*k*T, and Q = DKE, we get
C(ideal gas) = N*(3/2)k?T/?T = (3/2)nR .