ELI5-how can a gun pack so much power?

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ELI5-how can a gun pack so much power?

In: Physics
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Gunpowder is a chemical explosive. What does that mean, basically?

Well, it means that gunpowder is very unstable. Provided enough energy to give it a little “push” it will react with oxygen and release a bunch of energy as light and heat that it was storing in the chemical bonds holding it together.

This energy can provide that same “push” to more gunpowder nearby. This means that you can create a chain reaction where a bunch of powder all explodes in an instant. If we use this heat to push a bullet, we can make it go very, very fast. Fast moving projectiles are, well, very deadly.

By having an explosive transfer a ton of energy to a small, but fast moving piece of lead and copper: the bullet. That transfer of energy, from gunpowder to bullet, is then transfered again from bullet to target.

The energy is extreme because of the power of the explosive being focused into a tiny bit of mass, Nd then focused even more by that tiny bit of mass being pointed and designed to penetrate what it strikes.

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Say we make an air gun. We have a tank we pressurize to 4,000 psi and release it behind the bullet. The pressure pushes the bullet out of the barrel at a certain velocity. Velocity is limited by how much pressure we can put behind the bullet, but the air needs to be fed from some tank, and tanks start getting pretty heavy and bulky when the pressure goes up much more than that.

Guns are the same thing, only the pressure is generated by expanding gases released from the burning of gunpowder. The pressure generated by the gasses varies by cartridge, but a common 9mm pistol will be around 30,000 psi, and a .223 (AR-15) will be around 50,000 psi. That is a whole lot more pressure than an air gun, so the bullet comes out a lot faster. It’s not as bulky because only the chamber around the cartridge itself needs to contain that pressure.

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.