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Rec14_172Fall11 - Physics 172 Fall 2011 Recitation 14...

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Physics 172 – Fall 2011 Recitation 14 – Entropy and Temperature Problem 1 a) List explicitly all of the different ways that 2 quanta of vibrational energy can be arranged in 4 one-dimensional oscillators, that is, list all of the microstates of a 4 oscillator system in the macrostate with total vibrational energy 2 ω h . b) Verify that the total number of microstates, ! ( q , N ) , is equal to ( q + N ! 1)! q !( N ! 1)! , the general formula for this number derived in the text. c) If you make a sequence of 10,000 independent observations of the microstate of this system, about how many times do you expect to find it in the 0020 microstate? About how many times do you expect to find it in a microstate with 2 quanta in the same oscillator? About how many times do you expect to find it in a state in which no oscillator has more than one quantum of vibrational energy? [Checkpoint 1] Problem 2 Consider a nanoparticle consisting of 27 copper atoms. Recall that the molar mass of
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