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# Plot Cv/NkB vs kBT/hw
# The Einstein model of the solid predicts the heat capacity accurately at high temperatures,
# but noticeably deviates from experimental values at low temperatures.
import numpy as np
import pylab
T = np.linspace(0,2.,4000) # Create a temperature axis [0,2] with 4K equally spaced points
beta = 1./T # Calculate the reciprocal (hw/kBT) . hw=1, kB=1
Cv = beta*beta*np.exp(beta)/((np.exp(beta)-1)**2) # Calculate Cv
pylab.plot(T, Cv ,'-r') # Plot kBT/e vs Cv
pylab.xlabel('kB*T/hw'); pylab.ylabel('Cv= B^2*exp(beta)/(exp(beta)-1)^2')
pylab.show()
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