First-order phase transitions are characterized by a discontinuous first derivative of the Gibbs free energy, so that volumes and entropies are discontinuous. Such transitions are common in the crystalline state but extremely rare in liquid substances and experimentally evidenced in only one pure element, phosphorus. However, the microscopic nature and origin of the liquid-liquid transition in phosphorus is still debated. Here we report combined in situ X-ray diffraction, density and viscosity measurements along the first-order liquid-liquid transition line at high pressures and temperatures. We confirm that the transformation involves an abrupt density jump between two structurally distinct liquids and is associated to a drastic change of the viscosity. We accurately measured the temperature dependence of the density jump which exhibits a non-monotonic variation. This is explained by competing effects of entropy and density, as the order parameter for the transition includes both contributions.