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Question:

Why is a cold air intake in a car efficient but in a powerplant boiler the air is heated for more efficiency?

In a Babcock Wilcox boiler the air for combustion is preheated before being mixed with the fuel and I have been told that this decreases the amount of energy that is needed to heat the air to the correct temperature for combustion. This seems to contradict the whole concept of a cold air intake in a car in which cold air carries more molecules for a given volume thus providing better, more complete combustion.

Answer:

Apples and oranges. Boilers work by burning fuel to produce heat energy. Therefore, preheating the intake air by passing it through a heat-exchanger with the exhaust air results in energy savings. Engines work by compressing the fuel-air mixture, then combusting it to produce mechanical energy. Coolng the intake air makes it denser, and the engine can pack a larger quantity of fuel and air into the cylinder for each power stroke, making it more efficient.
I have a 2003 Nissan 350Z and I installed a cool air intake in my car, what it does is force cool air into the engine so the engine does not get to hot which aids the car in having more horsepower. They really do work well as long as you buy a good intake system. I have added 12-15 horse to my car, it may not seem like alot but you do feel it!
Steven gives you a good review of the situation but sadly misses the central issue in his answer to your question: There is no contradiction. The intake of cold air by the car engine is not more efficient; in fact (just like the boiler!) it is less so. The lower temperature of the air simply allows a higher mass flow of air which creates a need for more fuel (to reach the same hot gas temperature). This provides a higher output power than warmer air would, but not a higher efficiency!! Some of the extra fuel is needed to heat the air from its initially lower temperature up to the hot gas temperature! You may recall that it is the latter temperature which basically determines the efficiency (see Carnot). They sometimes boost the output power of gas turbines in power plants for peak loading by injecting water or steam into the burner, which basically does the same thing i.e. increases the mass flow. But it needs disproportionally more fuel input as well and the efficiency loses out quite badly. Note1:The bit about more complete combustion is folklore, not thermodynamics. You can have a correct mixture of fuel and air at any normal air temperature. Note 2. A lower ambient temperature should improve the car motor efficiency (Carnot again) a little but since much of the heat is rejected to the cooling water of which the temperature is held constant, this won't make much difference.

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