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A detailed analysis is given of the effects of common and recurringapproximations used in conventional superconductivity theories on thecondensation energy values, whose magnitudes are notoriously smaller than thoseof other energies as the superconducting energy gap and the chemical potential.These approximations come from using the density of states $N(\epsilon)$ andthe chemical potential $\mu(T)$ either constant or temperature-dependent,respectively. We use these approximations, a total of three, to calculate thecritical temperature $T_{c}$, the superconductor energy gap $\Delta(T)$, thechemical potential $\mu(T)$ and the thermodynamic potential $\Omega(T)$ whichare needed to obtain the condensation energy, and compare them with the exactcase, i.e., where no approximations are used. To do this, we use a ternaryBoson-Fermion theory of superconductivity composed of unbound electrons (orholes) as fermions plus two-electron and two-hole Cooper pairs, both as bosons.Although all these approximations lead to reasonable values of $T_{c}$ and$\Delta(T)$, the resulting thermodynamic and chemical potentials are quitedifferent, so that the condensation energy value could be incorrect. However,when $N(\epsilon)$ and $\mu(T)$ variables are used, together with a correctphysical interpretation of the condensation energy as the sum of thethermodynamic and chemical potential differences, it leads to a betteragreement with reported experimental data, compared to the one obtained whentaking them as constants, particularly so for low temperatures.

A Boson-Fermion theory that goes beyond the BCS approximations for superconductors