# Homework Help: Pressure and gas expansion

1. Oct 24, 2005

### thenewbosco

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, $$\gamma = 1.40$$. 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.
I am to use the work gone by the gas:
$$W = (\frac{1}{\gamma - 1})(PiVi - PfVf)$$
to calculate the initial pressure required.
I do not know though how to find the final volume and final pressure...

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

any help on this....thanks

2. Oct 25, 2005

### maverick280857

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 $P_{i}V_{i}^{\gamma} = P_{f}V_{f}^{\gamma}$.

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: Oct 25, 2005
3. Oct 25, 2005

### Gokul43201

Staff Emeritus
Bosco, you have 2 equations in 2 unknowns. What's the problem ?

4. Oct 25, 2005

### GCT

what is the distance for which the bullet was accelerated?

5. Oct 25, 2005

### thenewbosco

oh i forgot the distance is 50cm.

6. Oct 25, 2005

### GCT

so what's the change in volume?

7. Oct 25, 2005

### thenewbosco

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 dont know....

8. Oct 25, 2005

### thenewbosco

anybody?????????

9. Oct 26, 2005

### GCT

just use substitution, right?

10. Oct 26, 2005

### Tom Mattson

Staff Emeritus
bosco,

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