Liquid Nitrogen Cannon, 1H11.30

Topic and Concept:

• Newton's Third Law, [:Newtons3RDLaw#Recoil: 1H11. Recoil]

Location:

• Cabinet: [:MechanicsCabinet:Mechanic (ME)]

• Floor Item: ME, South Wall

attachment:CannonEq04-400.jpg

Abstract:

A homemade aluminum cannon with a 3" bore diameter and bore length of nearly 34" is mounted on two 24" bicycle wheels and shoots either rubber stoppers or bottles filled with sand to show recoil. The only propellant is the pressure buildup from the liquid nitrogen transitioning from liquid to gas.

Important Setup Notes:

• The rubber stoppers have a tendency to "Ricochet" off the wall and bounce into the audience or back to the cannon itself.

• This demonstration requires about .5 L of liquid nitrogen per shot.

• Be sure to leave at least 2 meters of room behind the cannon for recoil.

• Maximum recoil is approximately 3 meters, using the harden rubber stopper and having the barrel horizontal wrt the floor.

Setup and Procedure:

1. Select the firing angle(angle of the cannon barrel relative to the ground). An angle of 45° will give the farthest range.
2. Choose the desired projectile: soft stopper, hard stopper, or sand-filled bottle.
3. Make sure the gas bleeder valve that is situated on the barrel is in the open position, (handle parallel to the barrel).
4. Pour about 0.5 L of liquid nitrogen into the barrel.
5. Using the rubber mallet to pound in the projectile into the muzzle, tapered end first. The rubber stoppers can be pounded flush with muzzle.
6. Close the gas bleeder valve. This well allow the Nitrogen gas to build up.
7. Grab the gas bleeder valve assembly and tip the cannon muzzle down to let the liquid nitrogen to slosh up/down the bore to accelerate the evaporation of the liquid nitrogen.

8. Made sure that the cannon is aimed at the mat on the wall

9. You wont need to waiting too long, about 30 seconds or so. Once enough pressure has accumulated within the barrel, the projectile will shoot out with an extreme force and velocity.

Cautions, Warnings, or Safety Concerns:

• DO NOT fire cannon into audience.

• Rubber Stopper(s) can be shot out with enough force and velocity to "severely" dent drywall at a distant of 20 meters away from the cannon.

• Maximum rage is yet unknown, close to or more than 30 meters

Discussion:

After the valve is closed, the barrel becomes air-tight and nitrogen gas (pressure)is free to build. In general, the aluminum cannon is at room temperature (75 °F, 24 °C, or 297K) and liquid nitrogen has a temperature of (-321 °F, -196 °C, or 77K). Therefore, there is a quite a lot of heat available to cause the liquid nitrogen to boil rapidly and convert into gas. However, the amount of volume that nitrogen occupies when in a liquid state is miniscule compared to the volume it occupies when in a gas state. This ratio is 1 to 694 and is called the liquid to gas expansion ratio. Which basically states in this case that when liquid nitrogen boils(ie. goes to gas), it will fill a volume that is about 700 times larger and will do so very quickly.

The pressure is given by the ideal gas law: P = n*R*T / V where P is the gas pressure, n is the number of moles of gas within the container, R is the gas constant, T is the temperature of the gas, and V is the volume of the container. Will be using R = 0.082(L  atm  K⁻¹  mol⁻¹) and assuming the ambient air is at STP (P = 1 atm, T = 293 K), and that the liquid nitrogen comes to thermal equilibrium with the ambient air to room temperature. One should note that these is an idea case and that the barrel will cool done rapidly thus reducing the local ambient room temperature.

With this, the maximum possible pressure within the barrel can be calculated. The barrel has a length of 34.75" but the bore length is 34" or .864 m and a radius of 1.5" or .0381 m. However, when the stopper is pounded into the bore, the volume decrease. The thickness of the stopper is about 1.75". So then new bore length is 32.25" or 0.819 m. Thus the barrel has a volume of 3.735 L (assuming cylindrical geometry V = π * r² * L and converting to liters)).

Just after the barrel is sealed off from the atmosphere, there is .5 L of liquid nitrogen and therefore 3.235 L of air inside. Thus there are [(1 atm)*(3.235 L)] / [(.082 atm L mol^-1 K^-1)*(293 K)] = .135 mol of air in the barrel. Liquid nitrogen has a density of 807 g L^-1 therefore there are 404 g of liquid nitrogen in the bore. Nitrogen has a molar mass of 28 g mol^-1 so there are 14.4 mol nitrogen within.

"If" all the liquid transitions to a gas, assuming there was enough friction to keep the projectile in place, the pressure would rise to P_max = [(n_air + n_N2) * R * T] / V = [(14.65 mol)*(.082 atm L mol^-1 K^-1)*(293 K)] / (3.235 L) = 108.8 atm or 1,598.9 psi or 1102.4 N cm^-2!!! It is difficult to determine the magnitude of the friction between the projectile and aluminum. However, it is apparent that 108.8 atm of pressure is more than enough. So

When the projectile is shot, the cannon imparts a force on the projectile and the projectile imparts an equal but opposite force on the cannon as per Newton's third law. From the perspective of momentum conservation, the total amount of momentum in the cannon-projectile system is zero: P_projectile = -P_cannon. The extent of the cannon's recoil is much smaller than that of the projectiles rage due to the large mass differences - made apparent by Newton's second law F = m * a.

Videos:

• Demonstration video to come...

• [https://www.youtube.com/user/LectureDemostrations/videos?view=1 Lecture Demonstration's Youtube Channel]

References:

• The concept for our design was obtained from, [http://www.physics.uci.edu/~demos/mechanics.html U.C.I]; [http://www.physics.uci.edu/~demos/pdf/mechanics/1h11.30-liquid_nitrogen_cannon.pdf UCI's liquid_nitrogen_cannon.pdf].

• [http://chemistry.about.com/od/moleculescompounds/a/liquidnitrogen.htm LN2 Facts]

• [http://en.wikipedia.org/wiki/Ideal_gas_law Ideal Gas Law]

• [http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CE0QFjAA&url=http%3A%2F%2Fwww.physicslabs.umb.edu%2FPhysics%2Fsum07%2FExp4_182_Sum07.pdf&ei=c8ASUJDHMYnCrQGE0oDYBA&usg=AFQjCNFR6NkZdq8yJHL28AT1RdRbufa-Qg&sig2=c0oUGSpeaW30rgvX8iOswA Latent Heat (Al vs LN2)]

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