# Thermodynamics Homework

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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?

Start separating ln Q into pieces that include V and those that do not, ln Q ln no V N ln (V 2N B) P k B T ln Q P N 2 k B T 0 2 V 2N B V N2 P 2 (V 2N B) N k B T V N, T 2 N k B T N 2, V 2N B V 2 V 2.

In an Einstein crystal, one principal assumption is that each of the N atoms of the crystal vibrate independently about their lattice positions.

(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.

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.

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