Chemical abundances of about fifteen elements from oxygen to europium are measured in seven red giants of the two open clusters NGC 2360 and NGC 2447. The effective temperatures of the giants are determined spectroscopically by taking advantage of their known masses (~2 Mo in NGC 2360 and ~3 Mo in NGC 2447) and bolometric magnitudes. The average iron abundances we obtain for the two clusters are [Fe/H]=0.07 for NGC 2360 and [Fe/H]=0.03 for NGC 2447. Evolutionary stellar model calculations are performed in the mass range 1-4 Mo in order to analyze the surface Na and O abundances predicted after the first dredge-up. The sodium abundance shows a well defined correlation with stellar mass in the 2-3 Mo range. The agreement between our Na abundance determinations in NGC 2360 and our model predictions at 2 Mo is very good. In contrast, the overabundance in one of the three stars in NGC 2447 exceeds that predicted at 3 Mo by ~0.08 dex, which is significant compared to the observational error bars. The effects of core overshooting, convection prescription, metallicity and nuclear reaction rates on the Na surface predictions of our models are investigated. An oxygen deficiency relative to iron by 0.2 dex is measured in our stars, in disagreement with our model predictions. Assuming that the Sun is 0.1-0.3 dex enriched in oxygen relative to neighbor stars could explain the discrepancy., Comment: 11 pages, 8 figures, accepted for publication in Astronomy and Astrophysics