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Mass of object during heat exchange

  1. Aug 21, 2012 #1
    1. The problem statement, all variables and given/known data

    An aluminum container with a mass of 400 g contains 200 g of water at a temperature of 18°C. After a block of iron at a temperature of 90°C is placed in the water, the final temperature of the mixture changes to 28°C. Find the mass of the iron, assuming that there is no loss of heat to the surroundings.


    2. Relevant equations

    mass of aluminum = 0.40 g, heat capacity of aluminum = 910 J(kg.°C)
    mass of water = 0.20 g, heat capacity of water = 4200 J
    mass of iron = ? heat capacity of iron = 460 J

    (delta)t = change in temperature

    mAcA(delta)tA +mWcW(delta)tW + mIcI(delta)tI = 0



    3. The attempt at a solution

    This is the solution shown in the book:

    (0.40 kg) x (910 J/(kg.°C)) x (28°C - 18°C) + (0.20 kg) x (4200 J/(kg.°C)) x (28°C - 18°C) + (mI) x (460 J/(kg.°C)) x (28°C - 90°C) = 0

    3640 + 8400 - 28520 mI = 0
    12040 = 28250 mI
    mI = 0.422 kg


    What I want to know is where they got 3640 and 8400 from, when 0.40 x 910 = 364 and 0.20 x 4200 = 840. Why did they add a zero? Is this an error in the book? I also do not know where 28 520 is from. What am I missing...
     
  2. jcsd
  3. Aug 21, 2012 #2

    rock.freak667

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    Homework Helper

    (0.40 kg) x (910 J/(kg.°C)) x (28°C - 18°C) = 0.4 * 910*10 = 3640

    You are forgetting to multiply by the change in temperature i.e. 10.
     
  4. Sep 1, 2012 #3
    a block of aluminum 4 inch by 4 inch have and chamber of 1inch x 1 inch witch is heat faster the chamber or the whole block?
     
  5. Sep 1, 2012 #4

    rock.freak667

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    You should start a new thread with your question with all the relevant equations and terms in it. Otherwise, you are hijacking another person's thread which I think your question is not related to the OP's question.
     
  6. Sep 1, 2012 #5
    Hi Rock.freak667 what you mean I am hijacking onother person's thead,
    I just like to find out if a 1inch diameter long 4 inch heat faster then all aluminum block
    the block as reach the temperature of 100F can you help me ?
     
  7. Sep 1, 2012 #6

    rock.freak667

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    It means that you are posting a question in another person's thread which has nothing to do with your question.

    I advise you to start a new thread following the template so that you can input your question and what equations you think will be relevant.

    If you are at a loss with what equation would be relevant, look up heat transfer by conduction, as that is what you are essentially wanting to know.
     
  8. Sep 1, 2012 #7
    Thanks lot but do you know the answer? can you send to me? thanks
     
  9. Sep 1, 2012 #8

    rock.freak667

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    As per the forum rules, no on at PF can just give you the answer. You need to show some attempt at finding the answer. Once more, please start a new thread.
     
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