# Energy gap in superconductors

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?

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 $\exp(-E_g/T)$.
• @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. – lemon Aug 3 '17 at 17:42