The scaling theory of type I superconductors close to the critical point is discussed. In this theory the exponent α = 0, which signals a heat capacity with a symmetric logarithmic divergence (non-classical behavior) superimposed on a discontinuity (classical behavior). An explicit scaling model for the Gibbs potential dependence on the thermodynamic fields is presented. Consequences of this model concerning the heat capacity are worked out. The classical Rutgers formula is not valid in the presence of the logarithmic contribution. The correct formula is derived. New ways for detecting nonclassical (fluctuations driven) effects are suggested.