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1. Consider two isolated systems of non-interacting spins with NA = 8 and NB = 12. Their initial energies are EA = -4μB and EB = -4µB. The energy of an isolated system of N non-interacting spins with spin 1/2 and magnetic moment u in an external magnetic field B is E = Nı(−uB)+N(uB) where N₁ is spin up, N₁ is spin down, and N = N₁ + N₁. a. Solve for N₁ in terms of E and N. b. What is N₁A? What is N₁B? c. How many microstates are available for system A?

1. Consider two isolated systems of non-interacting spins with NA = 8 and NB = 12. Their initial energies are EA = -4μB and EB = -4µB. The energy of an isolated system of N non-interacting spins with spin 1/2 and magnetic moment u in an external magnetic field B is E = Nı(−uB)+N(uB) where N₁ is spin up, N₁ is spin down, and N = N₁ + N₁. a. Solve for N₁ in terms of E and N. b. What is N₁A? What is N₁B? c. How many microstates are available for system A?

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Statical Mechanics (Thermal and Statical Physics) Instruction: Write ALL the solutions of this (necessary or and not direct answer) Write also the equations that are needed to solve for a certain problem. Thank you.
1. Consider two isolated systems of non-interacting spins with NA = 8 and NB = 12. Their initial energies are EA = -4μB and EB = -4µB. The energy of an isolated system of N non-interacting spins with spin 1/2 and magnetic moment u in an external magnetic field B is E = Nı(−uB)+N(uB) where N₁ is spin up, N₁ is spin down, and N = N₁ + N₁. a. Solve for N₁ in terms of E and N. b. What is NTA? What is N₁B? C. How many microstates are available for system A? How many microstates are available for system B? d. e. What are the total microstates of the composite system? f. If the two systems are allowed to exchange energy with one another, what is the total microstate of the combined system? What is the total energy of the combined system?
Transcribed Image Text:1. Consider two isolated systems of non-interacting spins with NA = 8 and NB = 12. Their initial energies are EA = -4μB and EB = -4µB. The energy of an isolated system of N non-interacting spins with spin 1/2 and magnetic moment u in an external magnetic field B is E = Nı(−uB)+N(uB) where N₁ is spin up, N₁ is spin down, and N = N₁ + N₁. a. Solve for N₁ in terms of E and N. b. What is NTA? What is N₁B? C. How many microstates are available for system A? How many microstates are available for system B? d. e. What are the total microstates of the composite system? f. If the two systems are allowed to exchange energy with one another, what is the total microstate of the combined system? What is the total energy of the combined system?
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