Aviation, Temperature vs. Density Question

Obviously the hot air is being heated up, presumably by engine heat.

 

Your understanding is correct up to the point where something is heated up.

 

The density is only changed by a tiny amount. The purpose of the venturi is to reduce the pressure on a carbureted engine to draw fuel. There may be a two stage venturi as well as a tube the fuel flows out of that creates a vortice to further reduce pressure and draw more fuel. There's a mixture control that the pilot controls that also affects fuel flow, but I'm not sure how it's implemented.

The main effect of the heated air would be the amount of increase in pressure in the engine during combustion. Hotter air would gain less heat and the engine would not produce as much power, so the carburetor heater is only used to prevent icing in cold conditions.

 

The density of air is a function of both its temperature AND its pressure. Keep temperature the same, and density increases with pressure. Keep pressure the same, and density decreases with temperature. Change them both, and the results are complex.

When you take cold outside air and heat it in the shroud, you decrease its density. You may or may not increase its ambient pressure. This depends on the configuration of the heating system. When you pass that same cold outside air through a venturi, you increase its density and decrease its pressure on the throat of the venturi (the Bernoulli effect). This drop in pressure allows fuel to flow into the carb.

 

I should have stated changed by a small amount. The temperature factor would be related to the relative change in Kelvins (equal to celsius + about 273).

I'm not sure how much density or temperature is reduced when the presssure is reduced going through a venturi. How different are the temperatures on the Kelvin scale of the heated and non heated air? Assuming the pressure of the heated air is the same as the unheated air, then the density will be less by the ratio of the Kelvin temperatures (cold/hot), (and volume per unit mass would increase by hot/cold ratio) assuming air behaves like an ideal gas within that range of Kelvin temperature.