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

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Homework Statement


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.

image.jpg


Homework Equations


Ideal gas laws.

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?[/B]
 
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kaspis245 said:

Homework Statement


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.

Homework Equations


Ideal gas laws.

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?[/B]
Where did you get the formula Vplug = dπl ?
 
kaspis245 said:
V=Ssurface*length

V=2πr*l=dπl
That's not the formula for the volume of a cylindrical plug. In general, surface area × length ≠ volume :frown:
 
SteamKing said:
That's not the formula for the volume of a cylindrical plug. In general, surface area × length ≠ volume :frown:
I'm not sure what Ssurface is intended to mean, but what kaspis has actually done is circumference x length.
 
haruspex said:
I'm not sure what Ssurface is intended to mean, but what kaspis has actually done is circumference x length.
Whatever. It's not a volume.
 
Vplug=(d/2)2π=7.065cm3
Vfree space=30ml-7.065ml=22.935cm3
Ok?
 
kaspis245 said:
Vplug=(d/2)2π=7.065cm3
Vfree space=30ml-7.065ml=22.935cm3
Ok?
Notice how you squared a distance but showed the units as cm cubed. That should be a clue that your formula is wrong..
 
kaspis245 said:
Vplug=21.195cm3
Vfree space=8.805ml
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. :oops:
 
kaspis245 said:
Vplug=5.3ml
Vfree space=24.7ml
That's the correct volume for the plug. :smile:
 

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