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I have to compute the entropy, temperature and show that the total energy can be written as

E(T,N) = 3/2*N*hbar*omega*coth(hbar*omega/(2*kT))

I have found that the temperature can be written as

1/T = k/(hbar*omega)*ln([E/N*hbar*omega+3/2]/[E/N*hbar*omega-3/2])

by differentiating the entropy with respect to E. Next, I would like to show that the energy can be written as shown above:

1. (hbar*omega)/(k*T) = ln([E/N*hbar*omega+3/2]/[E/N*hbar*omega-3/2])

2. exp((hbar*omega)/(k*T)) = ([E/N*hbar*omega+3/2]/[E/N*hbar*omega-3/2])

but this last term doesnt give me any hyperbolic cotangens???

Any help or suggestions appreciated. Thanks in advance

Best

M

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# Homework Help: Writting total energy from temperature

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