How Do You Calculate the Initial Pressure in an Air Rifle Using Thermodynamics?

In summary, an air rifle shoots a lead pellet by allowing high pressure gas to expand. Initially, 12 cubic centimeters of air are admitted to the barrel. It behaves as an ideal gas, with gamma equal to 1.40. The air expands behind a 1.1 g pellet and pushes on it as a piston with cross sectional area 0.03 cm^2. The pellet emerges from the barrel with speed 120 m/s.
  • #1
thenewbosco
187
0
an air rifle shoots a lead pellet by allowing high pressure gas to expand.
This happens quickly so it is an adiabatic process. initially 12 cubic centimeters of air are admitted to the barrel. It behaves as an ideal gas, [tex]\gamma = 1.40[/tex]. The air expands behind a 1.1 g pellet and pushes on it as a piston with cross sectional area 0.03 cm^2. the pellet emerges from the barrel with speed 120 m/s.
I am to use the work gone by the gas:
[tex] W = (\frac{1}{\gamma - 1})(PiVi - PfVf)[/tex]
to calculate the initial pressure required.
I do not know though how to find the final volume and final pressure...

I thought to use [tex]PfVf^\gamma = PiVi^\gamma[/tex] but this does not seem to change anything for me i still need to know Vf...

any help on this...thanks
 
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  • #2
Can you relate the time rate of change of momentum of the pellet to the average force exerted on it? And who would exert it (rather what)?

Also while deriving the equation for work done in an adiabatic process, you have already taken into account that [itex]P_{i}V_{i}^{\gamma} = P_{f}V_{f}^{\gamma}[/itex].

Hold on a sec: you know the mass of the pellet, its initial and final speeds so you can calculate the the change in momentum. To calculate the force, you need to find the rate of change of momentum. You need either the acceleration of the pellet or the time it took to attain a speed of 120 m/s. I think something is missing here. But if I get some more ideas, I'll post them here soon.
 
Last edited:
  • #3
Bosco, you have 2 equations in 2 unknowns. What's the problem ?
 
  • #4
what is the distance for which the bullet was accelerated?
 
  • #5
oh i forgot the distance is 50cm.
 
  • #6
so what's the change in volume?
 
  • #7
i said that it was 12cm^3 (the initial volume admitted) + (0.03cm^2)(50)cm.

I would then put this into the Vf for final volume but i then need the final pressure which i don't know...
 
  • #8
anybody?
 
  • #9
just use substitution, right?
 
  • #10
bosco,

I've merged your two threads together. Don't post the exact same thread multiple times. Once is enough.
 

1. What is pressure?

Pressure is defined as the amount of force exerted on a given area. In other words, it is the force per unit area. The SI unit for pressure is the Pascal (Pa), but other commonly used units include atmospheres (atm) and pounds per square inch (psi).

2. How does pressure affect gas expansion?

According to the ideal gas law, pressure and volume are inversely proportional. This means that as pressure increases, the volume of a gas decreases and vice versa. When a gas is under high pressure, the molecules are closer together and have less room to move, resulting in a decrease in volume. On the other hand, when a gas is under low pressure, the molecules have more space to move, causing an increase in volume.

3. What is Boyle's Law and how does it relate to pressure and gas expansion?

Boyle's Law states that at a constant temperature, the volume of a gas is inversely proportional to its pressure. In other words, as pressure increases, volume decreases and vice versa. This law explains the relationship between pressure and gas expansion, as an increase in pressure leads to a decrease in volume and vice versa.

4. How does temperature affect pressure and gas expansion?

According to Charles' Law, at a constant pressure, the volume of a gas is directly proportional to its temperature. This means that as temperature increases, volume increases and vice versa. This law helps explain the relationship between temperature and gas expansion, as an increase in temperature leads to an increase in volume and vice versa.

5. How does the kinetic theory of gases explain pressure and gas expansion?

The kinetic theory of gases states that gases are made up of small particles (molecules or atoms) that are in constant, random motion. When these particles collide with each other or with the walls of a container, they exert a force, which is what we refer to as pressure. As more particles are added to a container, the number of collisions increases, resulting in an increase in pressure. This theory also explains gas expansion, as an increase in the speed of the particles (caused by an increase in temperature) leads to an increase in pressure and therefore, an increase in volume.

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