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2 2 h2 Note that only the second term in the above equation depends on T .Our specialists are ready to work with such disciplines: If the science or subject you are interested in is not on the list, ask us about it.As said previously, we are ready to help you at any moment.Substituting into the equation for the probability 1 2 ) pj qvib qvib qvib We have shown that the partition function for the harmonic oscillator is qvib 1 Insert this into the equation for the probability pj (1 ) (1 ) From the preceding equation we can see that for the ground state p0 (1 ) 1 Therefore, the fraction in the ground state is equal to this probability.f0 p0 1 1 T To find the fraction of harmonic oscillators in the ground state at different temperatures, first convert the fundamental vibrational frequency for N2 to . c (3 1010 cm )(2330 ) 6.99 1013 We can then obtain a value for : (6.626 J s)(6.99 1013 ) 3352 K k B 1.38 J This simplifies the equation for the fraction of harmonic oscillators to: f0 1 T 1 Insert the different temperatures for T to obtain the fraction in the ground state: Temperature (K) f0 300 0.9650 10.In the equation A and B are constants, the other variables have their usual meanings. (a) P V N k B T A2 N 2 N (b) P V 2 N k B T V B 2 2 (c) P m V N2 (V 2N B) NA!k B T 2 2 (d) P AVN2 (V 2N B) k B T N2 (e) P V (V 2N B) N k B 2 (f) P N V N N Bk B T V2 2 1 N (g) P N N k B T 2 V V 2 1 (h) 2B P N 3N k B T 2 V V N2 (i) P 2 (V 2N B) N k B T V Answer: Since we want the equation of state, calculate the pressure in terms of volume and ln Q temperature using P k B T N, T .Therefore, differentiating with respect to T produces the following: ln Q N, V 3N 2T Insert this result into the equation for h Ei given above: ln Q 3N 2 2 h Ei k B T k B T 2T N, V 3 h Ei N k B T 2 8.The following expresses the partition function of the system in terms of the partition functions of the individual particles (such as atoms or molecules), q N . For this to be true, it must be the case that there are many more particles than available states. Derive that the fraction of harmonic oscillators in the ground vibrational state is given f0 1 T .That branch is not easy for the student that is why the main aim of Assignment Expert is to provide real thermodynamics help.Thermodynamics help is specially created for those who needed in our attention.