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

  • Thread starter kaspis245
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  • #1
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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]
 

Answers and Replies

  • #2
SteamKing
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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.


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 ?
 
  • #3
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V=Ssurface*length

V=2πr*l=dπl
 
  • #4
SteamKing
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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:
 
  • #5
haruspex
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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.
 
  • #6
SteamKing
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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.
 
  • #7
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Vplug=(d/2)2π=7.065cm3
Vfree space=30ml-7.065ml=22.935cm3
Ok?
 
  • #9
haruspex
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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..
 
  • #10
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Vplug=21.195cm3
Vfree space=8.805ml
 
  • #11
SteamKing
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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:
 
  • #12
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Vplug=5.3ml
Vfree space=24.7ml
 
  • #13
SteamKing
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Vplug=5.3ml
Vfree space=24.7ml
That's the correct volume for the plug. :smile:
 
  • #14
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What now?
 

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