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Temperature Change

  1. Apr 22, 2007 #1
    1. The problem statement:
    A 5.00 x 10^2 kg object is attached by a rope through a pulley to a paddle-wheel shaft that is placed in a well-insulated tank holding 25.0 kg of water. The object is allowed to fall, causing the paddle wheel to rotate, churining the water. If the object falls a verticle distance of 1.00 x 10^2 m at constant speed, what is the temperature change of the water? (specific heat = 4186 J/kg and gravity = 9.81 m/s^2).




    2. Relevant equations:
    Heat Lost = Heat Gained
    Mm Cm (Ti-Tf) = Mw Cw (Tf-Ti)



    3. The attempt at a solution
    The instructor has not lectured on this type of problem but has asked us to read the text and give it a shot. I can't seem to find a way forward with this problem. Is this a calorimetry problem? If so, I don't understand why the distance the object fell and the fact that it fell at a constant speed is important. Any help will be appreciated...thanks in advance!
     
  2. jcsd
  3. Apr 22, 2007 #2

    Doc Al

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    Staff: Mentor

    Hint: Does the energy of the falling object change?
     
  4. Apr 22, 2007 #3

    AlephZero

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    Mechanical work and heat are two different forms of energy. So, think what "conservation of energy" means in this situation.

    Re the "constant speed", since the mass is not acclerating you know the tension on the rope is equal to the weight mg, so you can calculate the work done by the rope on the paddle wheel. If the mass was acclerating the tension in the rope would be different.
     
  5. Apr 22, 2007 #4
    Conservation of energy say that energy remains constant, although it may change forms; so I would say that at the top, the object had "potential energy" and at the bottom it had "kinetic energy". If my calculations are correct, the object has 490,500J of potential energy. Does this mean that the object introduces 490,500J of heat energy to the water? If so, wouldn't I have to know what the initial temp of the water to determine how much it would change?
     
  6. Apr 22, 2007 #5
    I believe that I can determine the work done by the rope on the paddle with the following equation:
    W=FdCos0
    So, the work done is:
    500(100)Cos 90 degress = 50,000

    I'm not sure how this applies to my problem though??
     
  7. Apr 22, 2007 #6

    Doc Al

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    Does the object's KE change as it falls?
    I didn't check your calculations, but that's the idea: The object transfers mechanical energy as it falls to the paddle, which in turn transforms that energy into "heat". (Note that AlephZero's advice is equivalent--understand what's he's saying.)
    No. To find the final temperature you'd need to know the initial temperature--but all you are asked to find is the change in temperature.
     
  8. Apr 22, 2007 #7

    Doc Al

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    With what force does the rope pull on the paddle? Reread AlephZero's post.
     
  9. Apr 22, 2007 #8
    I see that I made an error calculating the work done by the rope...I forget to multiply the mass by the gravity. After recalculating, I see that the work done by the rope is 490,500. I suppose that it is no coincidence that this is the same as the value I got for potential energy. So If the object introduces 490,500 jules of energy to the water, I now have to figure out how this much energy effects that temp of water...any clues!
     
  10. Apr 22, 2007 #9

    Doc Al

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  11. Apr 22, 2007 #10
    Doc Al...you are the man!!! With your help, I was able to solve the problem. I used the following formula: Q=cm(delta T)
    Of course I had to rearrange it to solve for "T" but when I did, I determined that the temperature change was 4.69 degress. I've got more problems to solve but thanks alot for helping me with this one!
     
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