1. Consider a system of two Einstein solids, A and B, each containing 4 oscillators, sharing...
1. Consider a system of two Einstein solids, A and B, each containing 4 oscillators, sharing a total of 4 units of energy. Assume that the solids are weakly coupled, and that the total energy is fixed. a. How many different macrostates are available to this system? b. How many different microstates are available to this system? c. Assuming that this system is in thermal equilibrium, what is the probability of finding all the energy in solid A? d. What is the probability of finding exactly half of the energy in solid A? e. Under what circumstances would this system exhibit irreversible behavior?
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1. Consider a system of two Einstein solids, A and B, each
containing 4 oscillators, sharing...
1. Consider a system of two Einstein solids, A and B, each containing 10 oscillators, sharing...
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...
Use a computer to reproduce the table and graph in Figure 2.4: two Einstein solids, each...
Use a computer to reproduce the table and graph in Figure 2.4: two Einstein solids, each containing three harmonic oscillators, with a total of six units of energy. Then modify the table and graph to show the case where one Einstein solid contains six harmonic oscillators and the other contains four harmonic oscillators (with the total number of energy units still equal to six) Assuming that all microstates are equally likely, what is the most probable macrostate, and what is...
In System I, two Einstein solids A and B are in thermal contact with each other...
In System I, two Einstein solids A and B are in thermal contact with each other but isolated from their environment. Consider the particular arrangement of System I shown below. System I YA = 6, NA = ܠܛ Einstein Solid A Einstein Solid B a) How many microstates of Einstein solid A correspond to the arrangement shown for System I? b) How many microstates of Einstein solid B correspond to the arrangement shown for System I? c) What is the...
Consider two Einstein solids A and B that can exchange energy (but not oscillators/particles) wit...
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)...
Consider two Einstein solids A and B, consisting of NA and NB oscillators (NA NB), that...
Consider two Einstein solids A and B, consisting of NA and NB oscillators (NA NB), that share a total of q units of energy between them (ga + qB = q), write an expression for the multiplicity of the entire interactive system as a function of qA AB (ga) At what value ofqA will the multiplicity ΩAB (ga) be a maximum? [Determine by setting the derivative of ΩABGA) with respect to qA equal to zero.]
A system is composed of two harmonic oscillators, each of natural frequency w, and having permissible...
A system is composed of two harmonic oscillators, each of natural frequency w, and having permissible energies "*1/2)w, where" is any non-negative integer. The total energy of the system is = 'hwo, where" is a positive integer. • For a given energy, how many microstates are available to the system? What is the entropy of the system? • A second system is also composed of two harmonic oscillators, each of natural frequency 2w,. The total energy of this system is...
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...
Use a computer to reproduce the table and graph in Figure 2.4: two Einstein solids, each containing three harmonic oscillators, with a total of six units of energy. Then modify the table and graph to show the case where one Einstein solid contains six harmonic oscillators and the other contains four harmonic oscillators (with the total number of energy units still equal to six) Assuming that all microstates are equally likely, what is the most probable macrostate, and what is...
In System I, two Einstein solids A and B are in thermal contact with each other but isolated from their environment. Consider the particular arrangement of System I shown below. System I YA = 6, NA = ܠܛ Einstein Solid A Einstein Solid B a) How many microstates of Einstein solid A correspond to the arrangement shown for System I? b) How many microstates of Einstein solid B correspond to the arrangement shown for System I? c) What is 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)...
Consider two Einstein solids A and B, consisting of NA and NB oscillators (NA NB), that share a total of q units of energy between them (ga + qB = q), write an expression for the multiplicity of the entire interactive system as a function of qA AB (ga) At what value ofqA will the multiplicity ΩAB (ga) be a maximum? [Determine by setting the derivative of ΩABGA) with respect to qA equal to zero.]
A system is composed of two harmonic oscillators, each of natural frequency w, and having permissible energies "*1/2)w, where" is any non-negative integer. The total energy of the system is = 'hwo, where" is a positive integer. • For a given energy, how many microstates are available to the system? What is the entropy of the system? • A second system is also composed of two harmonic oscillators, each of natural frequency 2w,. The total energy of this system is...
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