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Homework Help: Specific Heat Capacity Problem.(Please check.)

  1. May 3, 2006 #1

    A 0.050kg metal bolt is heated to an unknown initial temperature. It is then dropped into a beaker containing 0.15kg of water with an initial temperature of 21.0 C. The bolt and metal then reach a final temperature of 25.0 C. If the metal has a specific heat capacity of 899 J/kg*C, find the initial temperature of the metal.

    the solution is:

    Change in Temp of metal = (C of water *mass of water* Change in temp of water)/(C of metal*mass of metal)

    Change of temp. of metal = [(4186 J/kg*C)(0.15kg)(25C-21C)]/[(899 j/kg*C)(0.050kg)
    Change of temp. of metal = 55.87C

    Change in temperature = Final Temperature-Initial Temperature
    Initial Temperature = Final Temp.-Change in Temp
    = -30.87C

    i want to ask why is the answer +80.87C from the book, instead of -30.87C?

    i hope you could explain so i can also explain it to my students. is the sign of the answer has something to do with the HEAT REMOVAL and HEAT ABSORPTION?

    Last edited: May 3, 2006
  2. jcsd
  3. May 3, 2006 #2

    Doc Al

    User Avatar

    Staff: Mentor

    This is off by a minus sign. The net change in thermal energy of "metal + water" is zero, so:
    Change in Temp of metal = - (C of water *mass of water* Change in temp of water)/(C of metal*mass of metal)

    The change in temp of the metal is -55.87C, not +. (The metal cools down.)

    25C - (-55.87C) = +80.87C
    Just keep in mind that the "heat" gained by the water must equal the "heat" removed from the metal. In terms of Q: For the water, Q = + (it heats up); for the metal, Q = - (it cools down). The net Q is zero.
  4. May 3, 2006 #3

    thanks for the reply.
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