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According to this set of lecture notes, the first experimental evidence of an energy gap of order $T_{c}$ in superconductors was in 1955 when Corak et al. measured the specific heat of a superconductor and found that in the superconducting state the specific heat behaves as $$c_{s}=a \gamma T_{c} e^{-b T_{c}/T}$$ with $b \approx 1.5$ while in the normal state we have $$c_{n}=\gamma T \, .$$

I think I am missing something simple here, but I do not understand how this implies that there is a minimum excitation energy per particle $\approx 1.5 T_{c}$, can someone enlighten me?

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The specific heat is proportional to the density of electrons in the conduction band. And, in equilibrium, the electron density obeys the Fermi-Dirac distribution which, when a band gap exists, is well-approximated by the Boltzmann factor $\exp(-E_g/T)$.

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  • $\begingroup$ -1 besides quoting the wrong physical equation, you didn't explain the origin of the 1.5 factor. $\endgroup$ – KF Gauss Aug 2 '17 at 23:34
  • $\begingroup$ @user157879 In what way is the equation wrong? Moreover, the OP did not ask us to explain the origin of the 1.5, rather to explain how the $1.5T_c$ corresponds to a minimum energy excitation - which I did in terms of the band gap. $\endgroup$ – lemon Aug 3 '17 at 17:42

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