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This isn't as straightforward as it may at first seem so I'll spare you the lecture and go right to the Cliff's Notes... NOS itself doesn't burn but serves as a catalyst to support greater combustion. By allowing more fuel to be burned, NOS acts something like a chemical form of supercharging. Additionally, the cooling effect makes the intake charge more dense, which also adds power in a very similar manner. I'm no engineer so I don't claim to understand all the ins and outs, but if an engineer were to explain it to you, chances are you wouldn't understand it all anyway. I've been using NOS for years and never had a problem with adding power when I need it or reliability, since I rarely actually need more power than I already have. I hope this is helpful. :cheers:
Here's a little better explination. "NOS" or nitrous oxide is chemically N2O. When this goes into your engine and gets compressed the heat and pressure change the liquid N2O into gaseous nitrogen and oxygen. Fuel needs oxygen to burn and you now have an additional supply. Thus to keep the same A/F ration you would want to add more fuel to burn with the additional oxygen. When you burn more fuel you get more horsepower. The extra nitrogen is used to cushion the larger explosion in the combustion chamber. Using pure O2 would work too except the explosion would be too great and destroy the engine. The nitrogen provents this from happening.
There is a cooling effect of liquid N2O going into the intake, but the horsepower gain from that is a small bonus compared to the additional fuel you can burn.
I hope this helps give you a better idea of what happens. By the way I am an engineer.