Originally Posted by custardpsc
abgd - in short - yes. Performance suffers because warm air is less dense so less weight of air is inducted per cycle and it can expand less and exert less pressure on teh piston. Also the reduced mass flow rate affects the mixture although this could in theory be sorted out by leaning.
Not really - with mixture you can only set the fuel flow, which in terms affects fuel to air ratio, but you won't get 100% of rated power with carb heat to on, regardless of how you set mixture.
Rho = p/(R x T)
Carb heat reduces density of air just by increasing the temperature just as higher altitude reduces density of air by decreasing the pressure. Even with full throttle and mixture 50°F ROP for maximum power, the engine will not achieve its full rated power at altitudes higher than sea level (unless turbocharged), since the maximum engine output is more or less proportional to density of air entering the engine. The same goes for carb heat - once you set it to hot, the engine cannot achieve full rated power anymore.