Consider an isolated spin- paramagnet in an externally applied magnetic field, B. The system has a total of N spins, where n; of the spins are up. (a) Calculate the statistical weight of the state as a function of N and (b) Calculate the entropy of the system in terms of the statistical weight. (c) Find an approximate expression for the entropy when N is a large number using Stirling's formula.
Consider an isolated spin- paramagnet in an externally applied magnetic field, B. The system has a total of N spins, where n; of the spins are up. (a) Calculate the statistical weight of the state as a function of N and (b) Calculate the entropy of the system in terms of the statistical weight. (c) Find an approximate expression for the entropy when N is a large number using Stirling's formula.
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prioritize parts a-c please
Transcribed Image Text:5. Consider an isolated spin- paramagnet in an externally applied
magnetic field, B. The system has a total of N spins, where n, of the
spins are up.
(a) Calculate the statistical weight of the state as a function of N and
(b) Calculate the entropy of the system in terms of the statistical
weight.
(c) Find an approximate expression for the entropy when N is a
large number using Stirling's formula.
(d) The internal energy of this system is given by
U = (N – 2n;)H3B
Calculate the temperature, T, as a function of N, n; and B using
the statistical definition of temperature in terms of the entropy of
the system.
(e) Starting from
m
ƏB.
U,N
T
calculate the total magnetic moment of the system as a function
of U and B.
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