In spite of the relevance of Classical Cepheids as primary distance indicators, a general consensus on the dependence of the Period-Luminosity (PL) relation on the Cepheid chemical composition has not been achieved yet. From the theoretical point of view, our previous investigations were able to reproduce some empirical tests for suitable assumptions on the helium to metal relative enrichment, but those results relied on specific assumptions concerning the Mass-Luminosity relation and the efficiency of the convective transfer in the pulsating envelopes. In this paper, we investigate the effects of the assumed value of the mixing length parameter l/Hp on the pulsation properties and we release the assumption of a fixed Mass-Luminosity relation. As a whole, we show that our pulsation relations appear fully consistent with the observed properties of Galactic and Magellanic Cloud Cepheids, supporting the predicted steepening and brightening of the PL relations when moving from metal-rich to metal-poor variables. Moreover, we show that the distances inferred by the predicted PW relations agree with recently measured trigonometric parallaxes, whereas they suggest a correction to the values based on the Infrared Surface Brightness technique, as already found from an independent method. Finally, also the pulsation metal contents suggested by the predicted PW relations appear in statistical agreement with spectroscopic [Fe/H] measurements.
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