# How much the gas has increased the speed of the plug?

1. Apr 2, 2015

### kaspis245

1. The problem statement, all variables and given/known data
The cannon is made from V=30ml test tube completely closed with a plug (diameter d=1,5cm; length l=3cm; mass m=5g). Before closing the test tube, V'=1ml of water is poured into it. Room temperature is 20oC , pressure p=105 Pa , relative humidity is σ=20%. When the temperature in the test tube becomes t'=40oC the plug is shot. I need to find how much the escaping gas has increased the speed of the plug after it had been shot.

I know that the initial speed with which the plug starts to move is v=12.134m/s.

2. Relevant equations
Ideal gas laws.

3. The attempt at a solution
I know that:

Vplug=dπl=14.13 cm3
Vfree space=30ml-14.13ml=15.87ml
t/Vfree space=t'/V

What now?

2. Apr 2, 2015

### SteamKing

Staff Emeritus
Where did you get the formula Vplug = dπl ?

3. Apr 2, 2015

### kaspis245

V=Ssurface*length

V=2πr*l=dπl

4. Apr 2, 2015

### SteamKing

Staff Emeritus
That's not the formula for the volume of a cylindrical plug. In general, surface area × length ≠ volume

5. Apr 2, 2015

### haruspex

I'm not sure what Ssurface is intended to mean, but what kaspis has actually done is circumference x length.

6. Apr 2, 2015

### SteamKing

Staff Emeritus
Whatever. It's not a volume.

7. Apr 2, 2015

### kaspis245

Vplug=(d/2)2π=7.065cm3
Vfree space=30ml-7.065ml=22.935cm3
Ok?

8. Apr 3, 2015

### SteamKing

Staff Emeritus
9. Apr 3, 2015

### haruspex

Notice how you squared a distance but showed the units as cm cubed. That should be a clue that your formula is wrong..

10. Apr 3, 2015

### kaspis245

Vplug=21.195cm3
Vfree space=8.805ml

11. Apr 3, 2015

### SteamKing

Staff Emeritus
No, this is not correct.

The diameter of the plug = 1.5 cm x length = 3 cm.
The capacity of the entire test tube is only 30 ml. According to your calculations, it is taken up mostly by the plug, which is wildly improbable.

In the calculation you made in Post #7, you forgot to divide d by 2 when doing the arithmetic.

12. Apr 3, 2015

### kaspis245

Vplug=5.3ml
Vfree space=24.7ml

13. Apr 3, 2015

### SteamKing

Staff Emeritus
That's the correct volume for the plug.

14. Apr 4, 2015

What now?