# Muzzle velocity of a metallic hydrogen firearm

Related and linked to Metallic Hydrogen Propellant and Barrel length of a metallic hydrogen firearm.

In the two previous questions, I've explored different properties of a firearm that uses metallic hydrogen, this ones aims to find out the muzzle velocity of such a firearm.

As an example, lets use a bullet that weighs 7.9 grams propelled with 0.05 grams of metallic hydrogen shot out of a barrel that is 145mm inn length.

How would a worldbuilder calculate the muzzle velocity of such a firearm?

The formulas would also be appreciated so that I and any world builder who would like to use metallic hydrogen as a propellant have the nessacary resources.

• How many grains of propellant? You can get a wide range of muzzle velocities with the same bullet and barrel by changing the amount of propellant. Commented Jan 8, 2022 at 23:44

The cold will bother you.

OK. Some math! I have a bad habit of letting those decimal points slide around so anyone interested in checking the math - please do.

Metallic hydrogen: 0.7 g/cc

Mole of gas at STP = 22.4 l

Boiling point of hydrogen = -252 C

1 mole gas at -252C and 1 atm = 1735 cc

1 atm at STP = 0.191325 Mpa

1 mole gas at -252C and 1 cc = 175.8 Mpa

0.7 mole gas at -252C and 1 cc = 123 Mpa

1 Mpa = 145 psa. 123 Mpa = 17835 psi

So 2 cc of metallic hydrogen would give you 35670 psi

I had to convert to psi to use this fine chart of various guns and muzzle velocities.

http://closefocusresearch.com/calculating-barrel-pressure-and-projectile-velocity-gun-systems

I use the chart because muzzle velocity will depend on barrel length and projectile weight. The barrel pressures here are those generated by a standard propellant load for that gun type and I swapped in the pressure generated by the metallic hydrogen sublimation.

35670 psi is close to the 33601 psi for the 357 magnum with muzzle velociity of 1250 ft/sec.

I found that the 357 magnum has a bullet case capacity of 1.7 cc. We had to use 2 cc metallic hydrogen to get the same muzzle velocity. So for guns you might be better off using black powder.

The assumption I made that made the metallic hydrogen weak is the temperature. When you let a liquid (or solid) expand into a gas you have an increase in enthalpy and so a decrease in temperature. That is why a can of liquid air gets so cold when you discharge it. The more the expansion, the more the pressure drops. Given the phenomenal increase in volume with the phase change from solid to gas hydrogen I assumed the gas would be at the lowest temp that would allow the phase change to happen which is the boiling point of hydrogen. Low temperature gases occupy less space and so produce less pressure. Because it is so stinking cold it is not as energetic as the black powder at 0C.

More math, because Starfish says H+ gas will turn into H2 and heat up. And expand.

Heat of formation of H2 from H + H = -104 kJ / mole

Specific heat of H2 : 28.8 J / mole / degree K

-252 C = 21 K