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 Bc(0)/Tc √ γe and the specific heat jump at Tc versus the coupling strength 2∆/kBTc [∆ and Bc(0) are the zerotemperature values of the superconducting energy gap and the thermodynamic critical field, respectively, Tc is the transition temperature, and γe 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 Bc(0) and Tc, which holds for type-I superconducting materials.