Statistical mehcanics To let k = h = v = 1 for simplicity. Then the Einstein tem
ID: 3162659 • Letter: S
Question
Statistical mehcanics
To let k = h = v = 1 for simplicity. Then the Einstein temperature is T_Einstein = 1.0. The energy comes in units hv = 1. This will make the problem simpler to do numerically, and make the meaning of the results much more transparent. Take the energy of an oscillator level to be E_n = nhv. i.e., you can and should ignore the zero-point energy. A nanocluster consists of 501 identical oscillators. It has 1500 quanta. (The temperature is defined in terms of the microcanonical ensemble.) First, let's look at properties of the system in the microcanonical ensemble. Find 5 = In W and W where W is the number of states in the microcanonical ensemble. Find the energy per oscillator E_oso. Find the entropy per oscillator S_oac.Explanation / Answer
1. W is found by exponentiating.
2.The total energy is a de±nite quantum mechanical value
Nh= 1500 (neglecting zero-point energy, as instructed).
Since the 501 oscillators are identical, the average energy is
Eosc= 1500/501 = 2.994011976
3. Again, the oscillators are identical, so the entropy per oscillator is the total entropy dividedby the number of oscillators:
S_osc = (1120*787707135893965/501)
= 2.23710121184809175