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Lightning strikes tree. Energy is absorbed by tree. Sap evaporates. How much sap?

  1. Sep 22, 2009 #1
    1. The problem statement, all variables and given/known data

    A certain storm cloud has a potential of 1.50 x 10^8 V relative to a tree. If, during a lightning storm, 50.0 C of charge is transferred through this potential difference and 1.00% of the energy is absorbed by the tree, how much sap in the tree can be boiled away? Model the sap as water initially at 26.0°C. Water has a specific heat of 4186 J/(kg·C°), a boiling point of 100°C, and a latent heat of vaporization of 2.26 x 10^6 J/kg.


    2. Relevant equations

    I'm actually kinda iffy on all the equations, but I got several answers that WebAssign told me was wrong...

    3. The attempt at a solution

    Energy gain of 50.0 C of charge accelerated through potential difference of (1.50 x 10^8 V) is (50.0 C)(1.50 x 10^8 V) = 7.5 x 10^9 J.

    To vaporize 1 kilogram of sap requires mcΔT = (1 kg)(4186 J/kg K)(100 - 26 degrees C) = 3.098 x 10^(5) J to heat to 100 degrees C

    An additional 2.26 x 10^6 J for the state change from liquid to gas, for a total required energy of 3.098 x 10^(5) + 2.26 x 10^6 = 2.57 x 10^6 J.

    The total energy absorbed is 1% of 7.5 x 10^9 = 7.5 x 10^7 J, and at 2.57 x 10^6 J per kg needed, we are able to vaporize:

    (7.5 x 10^7 J)/(2.57 x 10^6 J/kg) = 29.19 kg of sap.

    WebAssign says it's wrong.

    Please tell me where I went wrong.
    It isn't due for a few days, I just wanted to get this assignment out of the way... Last question.

    Thanks!
     
  2. jcsd
  3. Sep 22, 2009 #2

    kuruman

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    Homework Helper
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    Re: Lightning strikes tree. Energy is absorbed by tree. Sap evaporates. How much s

    WebAssign is evil. I see nothing wrong with your solution - your method is OK and I verified your numbers. It may be a matter of sig figs or (perish the thought) the wrong calculated formula has been put into the problem. I suggest that you take your solution to your instructor and ask him/her to find what is wrong with it. Do this before the deadline.
     
  4. Apr 13, 2010 #3
    Re: Lightning strikes tree. Energy is absorbed by tree. Sap evaporates. How much s

    Sorry to bring up an old thread, but I was under the impression that the energy absorbed by the tree will be equal to 1/2QV, and not QV. I'd be curious to hear what others have to say about this.

    Thanks,

    Tom
     
  5. Apr 14, 2010 #4
    Re: Lightning strikes tree. Energy is absorbed by tree. Sap evaporates. How much s

    That would be true if you had a capacitor with 50C on it that you let completely discharge.
    The question doesn't say that the stormcloud completely discharges however.
     
  6. Apr 14, 2010 #5
    Re: Lightning strikes tree. Energy is absorbed by tree. Sap evaporates. How much s

    I see what you're saying. Thanks.
     
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