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Heat exchange in a bath

  1. Oct 15, 2014 #1
    1. The problem statement, all variables and given/known data
    An aluminum vessel of 500 gr contains 117.5 gr water at 200C. a piece of iron of mass 200 gr and 750C is thrown inside. what's the final temperature and the water equivalent of the vessel.

    2. Relevant equations
    Specific heat of aluminum: 0.217
    Specific heat of iron: 0.113

    3. The attempt at a solution
    ##(500\cdot 0.217+117.5)(t-20)=200\cdot 0.113 (75-t)\rightarrow t=25^0##
    The answer should be 230C.
    The water equivalent:
    ##500\cdot 0.217=m=108.5 gr##
    The answer should be 110 gr
     
  2. jcsd
  3. Oct 15, 2014 #2

    NascentOxygen

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    Staff: Mentor

    I make it 25°. The difference may be explained by use of S.H. values slightly different from those used by the textbook authors?
     
  4. Oct 15, 2014 #3

    Simon Bridge

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    Science Advisor
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    I'm seeing slightly different values for relative specific heats depending on where people round off or what standard they use or something or other.
    I'm also thinking - check the book values from the chapter or any examples they give.
     
  5. Oct 15, 2014 #4

    NTW

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    For the aluminum container..... 500 g * 0,217 * 293 K = 31791
    For the water............................ 117,5 g * 1 * 293 K = 34428
    For the iron............................... 200 g * 0,113 * 348 K = 7865

    Total .................................................................... = 74084

    Now, 74084 / ((500 *0,217)+(117*1)+(200*0,113)) = 298,6 K = 25,6 ºC
     
  6. Oct 15, 2014 #5
    I don't know this equation: mass (x) specific heat (x) deg. kelvin, what are the units of the result? calories? or is it just a mathematical trick, some kind of a mean.
    I only know: mass (x) specific heat (x) [itex]\Delta t[/itex]
     
  7. Oct 15, 2014 #6

    NTW

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    It's a 'weighted mean'. Useful for a lot of things. The units don't matter, but they are cal, since [grams * (cal/(grams * K)) *K] simplify to cal...
     
  8. Oct 15, 2014 #7
    Thanks
     
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