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- Consider Ω = αU^(αNV) Use the following steps to find T, U(T), and CV 1. Use quantum mechanics and some combinatorics to find an expression for the multiplicity,Ω , in terms of U, V, N, and any other relevant variables. 2. Take the logarithm to find the entropy, S. 3. Differentiate S with respect to U and take the reciprocal to find the temperature, T, as a function of U and other variables. 4. Solve for U as a function of T (and other variables). 5. Differentiate U(T) to obtain a prediction for the heat capacity (with the other variables held fixed).The characteristic vibrational temperature for chlorine (Cl₂) gas is 805 K. Calculate the fraction of chlorine molecules in the first excited vibrational state (v-1) when the temperature is 1610 K.Q2/ For the harmonic oscillator in classical limit, if the partition function is given by Z(B) = 1/(ßħw)N, find the entropy and internal energy. Q3/ Prove that F = -KTlnz .