Not all molecules in a fluid phase or atoms in a crystal, have the same mechanical energy ϵ . there is a distribution of energies in complex systems where the probability distribution is given by the boltzmann distribution law: pi=1qe−ϵi/kbt and where the partition function q=∑i=0me−ϵi/kbt. the thermodynamic internal energy is a measure of the average mechanical energy of a system, i. e. un=< ϵ> =∑i=0mpiϵi. the heat capacity on the other hand measures the energy disperion of the system and is therefore propotional to the variance of the energy: cv=nσ2ϵkbt2 where σ2ϵ=< ϵ2> −< ϵ> 2part a assume at t=298k only the four lowest vibrational energy levels of cl2 are populated. the four energy levels are non-degenerate and are separated by a constant energy spacing of δϵ=1.12×10−20j. calculate vibrational partition function for cl2 . at t=298k. assume the ground state energy ϵ0=0j .part b calculate the average vibrational energy < ϵ> at t=298kpart c calculate the average squared vibrational energy < ϵ2> part d calculate the molar vibrational heat capacity cv for cl2 at t=298k.