Two isolated boxes A and B each have single-particle energy levels 0,✏, 2✏, 3✏, 4✏, . . .. Box A contains two particles with total energy 2✏, whilst box B contains three particles with total energy 3✏...
Two isolated boxes A and B each have single-particle energy levels 0,✏, 2✏, 3✏, 4✏, . . .. Box A contains two particles with total energy 2✏, whilst box B contains three particles with total energy 3✏. The particles are distinguishable and do not interact with each other.
(a) Determine the total number of microstates ⌦A and ⌦B accessible to each box separately and show that the total number of microstates accessible to them jointly is, ⌦ = 30. 8
(b) The boxes are now put into thermal contact so that energy (but not particles) can be exchanged between them. Show that the new number of microstates accessible to the system is, ⌦⇤ = 126 . 8
(c) Calculate the change in entropy of the system resulting from the thermal contact. 4
(d) What is the new average energy of each box?
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Two isolated boxes A and B each have single-particle energy levels 0,✏, 2✏, 3✏, 4✏, . . .. Box A contains two particles with total energy 2✏, whilst box B contains three particles with total energy 3✏...
Ive calculated a,b need C and D , please can you show all workings Two isolated boxes A and B each have single-particle...
Ive calculated a,b
need C and D , please can you show all workings
Two isolated boxes A and B each have single-particle energy levels 0,e,2,3e,4e,.. Box A contains two particles with total energy 2, whilst box B contains three particles with total energy 3e. The particles are distinguishable and do not interact with each other (a) Determine the total number of microstates Ω. and Ωв accessible to each box sepa- rately and show that the total number of microstates...
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...
Question 3 a) Consider the hypothetical case of two degenerate quantum levels of energy E1, E2...
Question 3 a) Consider the hypothetical case of two degenerate quantum levels of energy E1, E2 (E. < Ez) and statistical weights g1 = 4, 92 = 2. These levels have respective populations N1 = 3 and N2 = 1 particles. What are the possible microstates if the particles are (1) bosons (6 marks) or (ii) fermions (6 marks)? AP3, PHA3, PBM3 PS302 Semester One 2011 Repeat page 2 of 5 b) Show how the number of microstates would be...
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)...
(TOTAL MARKS: 25) QUESTION 4 (15 marks] Q4(a) Assume 4 fermionic particles (N=N,+NA+N, -4) populate 3...
(TOTAL MARKS: 25) QUESTION 4 (15 marks] Q4(a) Assume 4 fermionic particles (N=N,+NA+N, -4) populate 3 degenerate energy levels E <E, <E, with 8, = 4,8, = 3.8, = 2 and N, 2N, 2N, What are the possible macrostates of this system ? (3 marks) (l) For each macrostate found at (), count the number of possible microstates using sketches showing the quantum state occupation number in each energy level. (7 marks) (H) Retrieve your results at (ii) if the...
We have 2 boxes, each containing 3 balls. Box number 1 contains one black and two...
We have 2 boxes, each containing 3 balls. Box number 1 contains one black and two white balls; box number 2 contains two black and one white ball. Our friend chooses one of the boxes at random, probability of choosing box number 1 is p. Then he takes one ball from a chosen box (each of three balls can be taken chosen equally likely), and it turns out to be white. We are going to find MAP estimate for the...
Problem 2. We have 2 boxes, each containing 3 balls. Box number 1 contains one black and two white balls; box nber 2 contains two black and one white ba Our friend chooses one of the boxes at ran...
Problem 2. We have 2 boxes, each containing 3 balls. Box number 1 contains one black and two white balls; box nber 2 contains two black and one white ba Our friend chooses one of the boxes at random, probability of choosing box number 1 is p. Then he takes one bal from a chosen box (each of three balls can be taken chosen equally likely), and it turns out to be white We are going to find MAP estimate...
3. Two boxes each contain three cards. The first box contains cards labelled-1,1 and 2; the...
3. Two boxes each contain three cards. The first box contains cards labelled-1,1 and 2; the second box contains cards labelled-2, -1 and 2. In a game, a player draws one card at random from each box and his score, W, is the product of the numbers on the two cards. w -4 -1 N 4 P(W =w) 1 9 3 9 1 1 9 a) Complete the above table. (4 marks) b) Find P(-2 SW 52). (2 marks) c)...
Ive calculated a,b
need C and D , please can you show all workings
Two isolated boxes A and B each have single-particle energy levels 0,e,2,3e,4e,.. Box A contains two particles with total energy 2, whilst box B contains three particles with total energy 3e. The particles are distinguishable and do not interact with each other (a) Determine the total number of microstates Ω. and Ωв accessible to each box sepa- rately and show that the total number of microstates...
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...
Question 3 a) Consider the hypothetical case of two degenerate quantum levels of energy E1, E2 (E. < Ez) and statistical weights g1 = 4, 92 = 2. These levels have respective populations N1 = 3 and N2 = 1 particles. What are the possible microstates if the particles are (1) bosons (6 marks) or (ii) fermions (6 marks)? AP3, PHA3, PBM3 PS302 Semester One 2011 Repeat page 2 of 5 b) Show how the number of microstates would be...
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)...
(TOTAL MARKS: 25) QUESTION 4 (15 marks] Q4(a) Assume 4 fermionic particles (N=N,+NA+N, -4) populate 3 degenerate energy levels E <E, <E, with 8, = 4,8, = 3.8, = 2 and N, 2N, 2N, What are the possible macrostates of this system ? (3 marks) (l) For each macrostate found at (), count the number of possible microstates using sketches showing the quantum state occupation number in each energy level. (7 marks) (H) Retrieve your results at (ii) if the...
We have 2 boxes, each containing 3 balls. Box number 1 contains one black and two white balls; box number 2 contains two black and one white ball. Our friend chooses one of the boxes at random, probability of choosing box number 1 is p. Then he takes one ball from a chosen box (each of three balls can be taken chosen equally likely), and it turns out to be white. We are going to find MAP estimate for the...
Problem 2. We have 2 boxes, each containing 3 balls. Box number 1 contains one black and two white balls; box nber 2 contains two black and one white ba Our friend chooses one of the boxes at random, probability of choosing box number 1 is p. Then he takes one bal from a chosen box (each of three balls can be taken chosen equally likely), and it turns out to be white We are going to find MAP estimate...
3. Two boxes each contain three cards. The first box contains cards labelled-1,1 and 2; the second box contains cards labelled-2, -1 and 2. In a game, a player draws one card at random from each box and his score, W, is the product of the numbers on the two cards. w -4 -1 N 4 P(W =w) 1 9 3 9 1 1 9 a) Complete the above table. (4 marks) b) Find P(-2 SW 52). (2 marks) c)...
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