Two perfect gases at absolute temperatures T1 and T2 are mixed.Assuming that there is no loss of energy.Find the temperature T of the mixture if the masses of the molecules are m1 and m1 and the number of molecules in the gases are n1 and n2.
According to the kinetic theory of gases, the kinetic energy of an ideal gas molecule at temperature T is given by K.E = 32kT. As there is no force of attraction among the molecules of a perfect gas, PE. of the molecules is zero.So the energy of a molecule of perfect gas is as follows:
E = K.E. + P.E. = 32kT + 0 = 32kT
Now, if T is the temperature of the mixture , by conservation of energy , we have
n1E1 + n2E2 = (n1+n2)E
or
n1(32 kT1) + n2(32 kT2) = (n1 + n2) 32kT ⇒ T=n1T1+n2T2n1 + n2