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In System I, two Einstein solids A and B are in thermal contact with each other...
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...
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...
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)...
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...
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.]
2. Consider a macroscopic system of two blocks that are in thermal contact. The two-block system ...
2. Consider a macroscopic system of two blocks that are in thermal contact. The two-block system is isolated from the rest of the universe. Initially, a hotter block is at a temperature TH and a colder block is at a temperature Tc. In the final state of the system, the two blocks are at the same intermediate temperature T. Compare the following quantities for the matal state and final state: Entropy for the block that starts at TH Sf> Si...
The system above has two distinguishable particles, each can be in either of two boxes. The...
The system above has two distinguishable particles, each can be
in either of two boxes. The system is in thermal equilibrium with a
heat bath at temperature, T. The energy of the particle is zero
when it's in the left box, and it is
when it is in the right box. There is a correlation energy term
that increases the system energy by
if the particles are in the same box.
If the particles are indistinguishable how many microstates will...
3.3 One spin in thermal contact with a large spin system Generalize the preceding problem by...
3.3 One spin in thermal contact with a large spin system Generalize the preceding problem by considering the case where the system A' consists of some arbitrarily large number N of spins J, each having magnetic moment plo. The system A consists again of a single spin { with mag- netic moment Mo. Both A and A' are located in the same magnetic field B and are placed in contact with each other so that they are free to exchange...
I’m horrible with probabilities so please help me and also show work so I could understand...
I’m
horrible with probabilities so please help me and also show work so
I could understand them
Part A Suppose you toss a coin and it lands flat on the table. There are two possible final states for the coin, it can land with heads up or tails up. Now consider tossing three coins, one after the other. How many different arrangements are possible? Hint: Four of the possible arrangements are shown below. H HT HTH THH Part B We...
As it is shown in the figure above, there's a system of three chambers, each of which has the vol...
This question is related to thermal physics by Kittel.
As it is shown in the figure above, there's a system of three chambers, each of which has the volume v. Initially there's only A particles in chamber l; B particles in chamber II, and C while wall between chamber ll and Ill is only permeable to particle C. All thhree types of particles can be treated as ideal gases. The number of particles are denoted by NA, NB, NC a)...
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)...
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...
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.]
2. Consider a macroscopic system of two blocks that are in thermal contact. The two-block system is isolated from the rest of the universe. Initially, a hotter block is at a temperature TH and a colder block is at a temperature Tc. In the final state of the system, the two blocks are at the same intermediate temperature T. Compare the following quantities for the matal state and final state: Entropy for the block that starts at TH Sf> Si...
The system above has two distinguishable particles, each can be
in either of two boxes. The system is in thermal equilibrium with a
heat bath at temperature, T. The energy of the particle is zero
when it's in the left box, and it is
when it is in the right box. There is a correlation energy term
that increases the system energy by
if the particles are in the same box.
If the particles are indistinguishable how many microstates will...
3.3 One spin in thermal contact with a large spin system Generalize the preceding problem by considering the case where the system A' consists of some arbitrarily large number N of spins J, each having magnetic moment plo. The system A consists again of a single spin { with mag- netic moment Mo. Both A and A' are located in the same magnetic field B and are placed in contact with each other so that they are free to exchange...
I’m
horrible with probabilities so please help me and also show work so
I could understand them
Part A Suppose you toss a coin and it lands flat on the table. There are two possible final states for the coin, it can land with heads up or tails up. Now consider tossing three coins, one after the other. How many different arrangements are possible? Hint: Four of the possible arrangements are shown below. H HT HTH THH Part B We...
This question is related to thermal physics by Kittel.
As it is shown in the figure above, there's a system of three chambers, each of which has the volume v. Initially there's only A particles in chamber l; B particles in chamber II, and C while wall between chamber ll and Ill is only permeable to particle C. All thhree types of particles can be treated as ideal gases. The number of particles are denoted by NA, NB, NC a)...
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