Looking at the cruise performance tables in the POH of the C150, C172 or C182, one can see that for the same pressure altitude, the same RPM and the same true airspeed, the fuel consumption is reduced at higher temperature.
For example, a 1976 C150 POH indicates, at 2500 RPM, at 2000 ft pressure altitude,
- at -5°C: 97 KTAS, 5.3 GPH
- at 15°C: 96 KTAS, 4.9 GPH
- at 35°C: 95 KTAS, 4.6 GPH
(yes, there is a 1 kt difference each time, but interpolating the values gives very similar results)
But thermodynamics tells us that the efficiency is proportional to the difference of temperature between the isothermal expansion at Th and the isothermal compression at Tc in the Carnot cycle, thus efficiency = (Th-Tc)/Th.
I cannot reconcile the consumption data with that theory, since apparently the output power is the same (true airspeed, with identical parasitic and induced drag forces) for an apparently higher efficiency at higher Tc temperature.
What other factor am I missing?