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(a) TRUE (b) FALSE Answer: We had to assume that the number of available states was greater than the number of particles. Then, given that for N2 is 2330 , calculate f0 for N2 (g) at 300 K and K.

(a) and 0.7457 (b) and (c) and 0.9650 (d) and (e) 0.9578 and 0.8762 (f) 0.9200 and 0.4578 Answer: To find an expression for the probability that a harmonic oscillator will be found in the jth state, start with the general equation for the probability pj qvib where Ej 12 ) for a harmonic oscillator.

The crystal is thus pictured in three dimensions as N independent three dimensional harmonic oscillators.

Using the partition function for a harmonic oscillator, qho (T ) X e 12 X , determine the partition function for an Einstein crystal.

Homework can be really stressful for many students.

To deal with it, sometimes, you have to give up spending time at home with your family or going out with friends.It will be helpful to make use of the geometric series, X xj 1 to derive this result.e (a) Q (b) Q (c) Q (d) Q (e) Q (f) Q 1 Answer: The partition function for a harmonic oscillator is given as qho (T ) X e 21 X If we let x we can simplify the partition function to qho (T ) X Note that this summation is the geometric series, X xj X 1 . The average energy for a monatomic van der Waals gas is 3 a NA2 h Ei NA k B T 2 V Use the definition of the constant volume molar heat capacity discussed in lecture video 3.4 to determine a formula for the constant volume molar heat capacity of a monatomic van der Waals gas.Determine the average energy, h Ei, for a monatomic ideal gas given the partition function for this gas, 1 Q(N, V, T ) N! N V h Ei k B T (c) h Ei k B T 2 (d) h Ei k B T N V (e) h Ei k B T 3N 2 (f) h Ei h2 N V 3N 2T Answer: First, rearrange this equation, 1 Q(N, V, T ) T N! Take the natural log of both sides of the partition function and separate the terms to obtain 3N 3N ln T ln N ln V ln Q(N, V, T ) N !2 2 h2 Note that only the second term in the above equation depends on T .University of Minnesota Statistical Molecular Thermodynamics Homework Week 3 1.You are given the following partition function for a fictitious gas What is the correct equation of state for Vikonium?Here, NA is number and R is the universal gas constant.(a) 23 NA k B (b) (c) 2 a N 23 NA k B T V A 23 NA k B a NA2 2 a N 3 2R VA 23 R 43 RT 2 (g) CV 34 NA k B T 2 (d) (e) (f) 2T a NA V (h) a) and e) (i) b) and g) (j) none of the above Answer: The molar heat capacity is defined in lecture video 3.4 as U N, V N, V Insert the average energy that is given 3 a NA2 h Ei NA k B T 2 V into the expression for the heat capacity: 2 Ei 3 a N A NA k B T N, V 2 V Differentiating with respect to temperature gives the heat capacity for a monatomic van der Waals gas as 3 NA k B 2 Substituting R NA k B , we can also see that 3 R 2 This heat capacity is the same as that for a monatomic ideal gas. In the lecture videos, a general formula for the average energy, ln Q 2 h Ei k B T , N, V was derived.At a fixed temperature this means that the partition function will increase.Thermodynamics is a branch of physics which studies the laws of govern the conversion of energy from one form to another.

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