Equal number of molecules of an ideal monatomic and an ideal diatomic gas are at the same temperature. Which gas will be more heated if equal amount of heat is supplied from outside?

Explanation

Let N=Number of molecules in each of the gases kept at a temperature T. Degrees of freedom of an ideal monatomic molecule=3.
So the average kinetic energy of the monatomic gas `E_1=3/2NkT`, then its heat capacity at constant volume, `C_(v_1)=3/2 Nk`. [k= Boltzman constant]
Similarly, for the diatomic gas `C_(v_2)=5/2Nk` as the number of degrees of freedom of a diatomic molecule =5.
Now an amount of energy E, in the form of heat,is supplied to each of the gases, IF `T_1` and `T_2` be the increases in temperature, respectively then
`E=C_(v_1) T_1=C_(v_2) T_2`,
or,`T_1/T_2=C_(v_2)/C_(v_1)=(5/2Nk)/(5/2Nk)=5/3`
So, `T_1 gt T_2` i.e., this monatomic gas will be more heated.