Homework Answers
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...
Q.7) Consider a systems of N>>1 identical, distinguishable and independent particles that can be placed in...
Q.7) Consider a systems of N>>1 identical, distinguishable and independent particles that can be placed in three energy levels of energies 0, E and 2€, respectively. Only the level of energy sis degenerate, of degeneracy g=2. This system is in equilibrium with a heat reservoir at temperature T. a) Obtain the partition function of the system. b) What is the probability of finding each particle in each energy level? c) Calculate the average energy <B>, the specific heat at constant...
Consider a system of two particles and assume that there are only two single-particle energy levels...
Consider a system of two particles and assume that there are only two single-particle energy levels ε1, ε2. By enumerating all possible two-body microstates, determine the partition functions if these two particles are (a) distinguishable and (b) indistinguishable.
Thermodynamics 5. A system has three energy eigenstates (microstates), with energies 0, E1, and E2 »...
Thermodynamics
5. A system has three energy eigenstates (microstates), with energies 0, E1, and E2 » Ei. It is sitting in a heat bath (reservoir) with temperature T. a. Find the partition function Z(T). b. Find simple approximate expressions for Z when t > E2, E2 »T» Ei, and T < E1. For the high- and medium-temperature regimes, your expressions should be zeroth-order, i.e., should not contain t, but for the low-temperature regime you should include the leading T-dependence. c....
Consider a system of 1000 particles that can only have two energies, E1 and E2 with...
Consider a system of 1000 particles that can only have two energies, E1 and E2 with E2>E1. The difference in the energy between these two values is delta E= E2-E1. Asume g1=g2=1. a) graph the number of paricle n1, n2 in states of E1 E2 as a function of kbT/deltaE, where kb is Boltzmann constant. Explain the result b) at what value kbT/deltaE do 750 of the particles have the energy E1
You are studying a system that has five evenly spaced energy levels. The lowest energy level (lab...
You are studying a system that has five evenly spaced energy levels. The lowest energy level (labeled "1") has an energy of 0.5 J. The remaining energy levels (labeled 2-5 in increasing energy) are evenly spaced, with 1 J energy spacing between the levels There are three particles in the system, and any number of particles can occupy each of the energy levels. If the average energy per particle is 3.5 J, as in the four questions above, how can...
Problem 6.15. Mean energy of a toy model of an ideal Bose gas (a) Calculate the...
Problem 6.15. Mean energy of a toy model of an ideal Bose gas (a) Calculate the mean energy of an ideal gas of N 2 identical bosons in equilibrium with a heat (b) Calculate the mean energy for N 2 distinguishable particles assuming that each particle can (c) If E1 is the mean energy for one particle and Eg is the mean energy for the two-particle system, bath at temperature T, assuming that each particle can be in one of...
Consider a system of 1000 particles that can only have two energies, E1 and E2, with...
Consider a system of 1000 particles that can only have two energies, E1 and E2, with E2 > E1. The difference in the energy between these two values IS Δ E2-E1. Assume g1 = g2-1. . Assume ga2- a) Graph the number of particles, nı and n2, in states E1 and E2 as a function of kBT AE, where ks is Boltzmann's constant. Explain your result. b) At what value of kBT /AE do 750 of the particles have the...
Consider a collection of N indistinguishable molecules with only two energy levels: E2 = E _________________...
Consider a collection of N indistinguishable molecules with only two energy levels: E2 = E _________________ g = 4 E1 = 0 _________________ g = 2 Derive an expression for S, the entropy of this system. Be sure to indicate clearly all of the important steps in the derivation.
A system consists of N weakly interacting subsystems. Each subsystem possesses only two energy levels E1...
A system consists of N weakly interacting subsystems. Each subsystem possesses only two energy levels E1 and E2 each of them non-degenerate. (i) Draw rough sketches (i.e. from common sense, not from exact mathematics) of the temperature dependence of the mean energy and of the heat capacity of the system. (ii) Obtain an exact expression for the heat capacity of the system. Very Detailed Explanation please.
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...
Q.7) Consider a systems of N>>1 identical, distinguishable and independent particles that can be placed in three energy levels of energies 0, E and 2€, respectively. Only the level of energy sis degenerate, of degeneracy g=2. This system is in equilibrium with a heat reservoir at temperature T. a) Obtain the partition function of the system. b) What is the probability of finding each particle in each energy level? c) Calculate the average energy <B>, the specific heat at constant...
Thermodynamics
5. A system has three energy eigenstates (microstates), with energies 0, E1, and E2 » Ei. It is sitting in a heat bath (reservoir) with temperature T. a. Find the partition function Z(T). b. Find simple approximate expressions for Z when t > E2, E2 »T» Ei, and T < E1. For the high- and medium-temperature regimes, your expressions should be zeroth-order, i.e., should not contain t, but for the low-temperature regime you should include the leading T-dependence. c....
You are studying a system that has five evenly spaced energy levels. The lowest energy level (labeled "1") has an energy of 0.5 J. The remaining energy levels (labeled 2-5 in increasing energy) are evenly spaced, with 1 J energy spacing between the levels There are three particles in the system, and any number of particles can occupy each of the energy levels. If the average energy per particle is 3.5 J, as in the four questions above, how can...
Problem 6.15. Mean energy of a toy model of an ideal Bose gas (a) Calculate the mean energy of an ideal gas of N 2 identical bosons in equilibrium with a heat (b) Calculate the mean energy for N 2 distinguishable particles assuming that each particle can (c) If E1 is the mean energy for one particle and Eg is the mean energy for the two-particle system, bath at temperature T, assuming that each particle can be in one of...
Consider a system of 1000 particles that can only have two energies, E1 and E2, with E2 > E1. The difference in the energy between these two values IS Δ E2-E1. Assume g1 = g2-1. . Assume ga2- a) Graph the number of particles, nı and n2, in states E1 and E2 as a function of kBT AE, where ks is Boltzmann's constant. Explain your result. b) At what value of kBT /AE do 750 of the particles have the...
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