  It is proven that there exist some universal relations between the energy gap
and the differences of the thermodynamic potential, entropy, specific heat and
critical magnetic field for many two- and three-dimensional models of
superconductivity with spin-singlet Cooper pairs forming \textit{s} or
\textit{d} or \textit{g} etc. states. The obtained formulae make it possible to
derive thermodynamic functions and, in particular, the superconducting specific
heat and the critical magnetic induction in the whole temperature range $0\leq
T\leq T_{c}$ employing the form of $\Delta(T)$ only. The inverse formula
allowing us to find $\Delta(T)$, when the temperature dependence of the
specific heat difference is known, is also presented. The results are referred
to some obtained within the McMillan formalism, and some remarks on an
application of the present formulae to the {\textit{t--J}} model are given.
