ELI5-how can a gun pack so much power?
In: Physics
Let’s distinguish between energy and power. Energy, when it comes to gunpowder, is simply determined by the amount of gunpowder, which has certain fixed amount of *heat of combustion*, that is amount of heat (which is energy) released by the chemical reaction, per unit of mass. There are many kinds of gunpowder but they all have more or less the same heat of combustion which is about 3000 joules per gram. Note that this is less than 1/10 of the heat of combustion contained in regular gasoline.
Power, on the other hand, is a rate of change of energy. Change can be any change, such as release, transfer, transformation or absorption of energy. In case of both gunpowder and gasoline we are talking about *exothermal* reaction so the rate of change will be rate of *release of energy*, in other words – the speed of burning.
Consider the most common pistol round, the 9×19 mm parabellum. The case of that round is typically loaded with anywhere between 3-7 grains of powder. Let’s assume 5 grains, or 0.324 mg. Such amount of powder releases 972 J of energy, of which about 50% is transferred to the bullet (the system comprised of the powder, bullet and the barrel is a heat engine and therefore has Carnot law limited efficiency).
Now, that reaction (of powder burning) takes a very short time, on the order of 1 milisecond. That means that the power released inside the barrel approaches 1 MW!
For comparison, a pretty powerful crossbow that accelerates an arrow within about 6.6 ms to velocity of 117 m/s endows that arrow with kinetic energy of only 179 joules and therefore releases power in the amount of only 27 kW. An arrow loosed from a typical recurve bow has even less energy, around 80 J, half the velocity and less than half the power.
So the short answer to your question is: guns pack so much power because of high mass energy density of the gunpowder (much higher than stress energy stored in a bow or crossbow limbs) and high rate of reaction.
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