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

  1. Apr 2, 2015 #1
    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.

    image.jpg

    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. jcsd
  3. Apr 2, 2015 #2

    SteamKing

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    Where did you get the formula Vplug = dπl ?
     
  4. Apr 2, 2015 #3
    V=Ssurface*length

    V=2πr*l=dπl
     
  5. Apr 2, 2015 #4

    SteamKing

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    That's not the formula for the volume of a cylindrical plug. In general, surface area × length ≠ volume :frown:
     
  6. Apr 2, 2015 #5

    haruspex

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    I'm not sure what Ssurface is intended to mean, but what kaspis has actually done is circumference x length.
     
  7. Apr 2, 2015 #6

    SteamKing

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    Whatever. It's not a volume.
     
  8. Apr 2, 2015 #7
    Vplug=(d/2)2π=7.065cm3
    Vfree space=30ml-7.065ml=22.935cm3
    Ok?
     
  9. Apr 3, 2015 #8

    SteamKing

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  10. Apr 3, 2015 #9

    haruspex

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    Notice how you squared a distance but showed the units as cm cubed. That should be a clue that your formula is wrong..
     
  11. Apr 3, 2015 #10
    Vplug=21.195cm3
    Vfree space=8.805ml
     
  12. Apr 3, 2015 #11

    SteamKing

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    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:
     
  13. Apr 3, 2015 #12
    Vplug=5.3ml
    Vfree space=24.7ml
     
  14. Apr 3, 2015 #13

    SteamKing

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    That's the correct volume for the plug. :smile:
     
  15. Apr 4, 2015 #14
    What now?
     
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