Homework Answers
The most probable macrostate is the one with the highest number of microstates since all microstates are equally likely to occur.
Therefore, qA = qB = 3 is the most probable macrostate and its probability is: P = 100/462 = 0.2164 = 21.64%
The least probable macrostate is the one with the lowest number of microstates.
Therefore, qA = 0 and qB = 6 or vice-versa are the least probable with probability: P = 28/462 = 0.0606 = 6.06%.
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Use a computer to reproduce the table and graph in Figure 2.4: two Einstein solids, each...
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Consider two Einstein solids A and B that can exchange energy (but not oscillators/particles) wit...
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1. Consider a system of two Einstein solids, A and B, each containing 10 oscillators, sharing a total of 20 units of energy. Assume that the solids are in thermal contact (and can, therefore, exchange energy units) and that the total energy is fixed. How many different macrostates are available to this system? a. b. How many different microstates are available to this system? Assuming that this system is in thermal equilibrium, what is the probability of finding all the...
Using matlab, evaluate the following system:Consider two Einstein solids \(A\) and \(B\) that can exchange energy (but not oscillators/particles) with one another but the combined composite system is isolated from the surroundings. Suppose systems \(A\) and \(B\) have \(N_{A}\) and \(N_{B}\) oscillators, and \(q_{A}\) and \(q_{B}\) units of energy respectively. The total number of microstates for this macrostate for the macrostate \(N_{A}, N_{B}, q, q_{A}\) is given by$$ \Omega\left(N_{A}, N_{B}, q, q_{A}\right)=\Omega\left(N_{A}, q_{A}\right) \Omega\left(N_{B}, q_{B}\right) $$where$$ \Omega\left(N_{i}, q_{i}\right)=\frac{\left(q_{i}+N_{i}-1\right) !}{q_{i} !\left(N_{i}-1\right)...
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