The temperature dependent measurements of the thermodynamic critical field and the specific heat for the pressure stabilized Ga-II phase of elemental Gallium are presented. The discussion of these and other Ga phases data in the context of elemental and binary phonon-mediated type-I superconductors allowed to establish simple scaling relations between BCS quantities such as $B_{rm c}(0)/T_{rm c}sqrt{gamma_{rm e}}$ and the specific heat jump at $T_{rm c}$ versus the coupling strength $2Delta/k_{rm B} T_{rm c}$ [$Delta$ and $B_{rm c}(0)$ are the zero-temperature values of the superconducting energy gap and the thermodynamic critical field, respectively, $T_{rm c}$ is the transition temperature, and $gamma_{rm e}$ is the electronic specific heat]. The scaling relations can be analytically expressed by taking into account strong-coupling corrections to BCS theory. Such correlations can naturally explain the linear relation between $B_{rm c}(0)$ and $T_{rm c}$, which holds for type-I superconducting materials.
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