The spectral properties of blazars seem to follow a phenomenological sequence according to the source luminosity. By inferring the source physical parameters through (necessarily) modeling the blazar spectra, we have previously proposed that the sequence arises because the particles responsible for most of the emission suffer increasing radiative losses as the luminosity increases. Here we extend those results by considering the widest possible range of blazar spectral properties. We find a new important ingredient for shaping the spectra of the lowest power objects, namely the role of a finite timescale for the injection of relativistic particles. Only high energy particles radiatively cool in such timescale leading to a break in the particle distribution: particles with this break energy are those emitting most of the power, and this gives raise to a link between blazar spectra and total energy density inside the source, which controls the cooling timescale. The emerging picture requires two phases for the particle acceleration: a first pre-heating phase in which particles reach a characteristic energy as the result of balancing heating and radiative cooling, and a more rapid acceleration phase which further accelerate these particles to form a power law distribution. While in agreement with standard shock theory, this scenario also agrees with the idea that the luminosity of blazars is produced through internal shocks, which naturally lead to shocks lasting for a finite time.
