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Specific Heat Capacity of Ice, Help!

  1. Feb 9, 2010 #1
    1. The problem statement, all variables and given/known data

    The following data is obtained:
    Weight of ice cube added 20 g
    Weight of copper calorimeter 80.5 g
    Weight of water in calorimeter 105 g
    Initial temp of ice cube -18 deg C
    Initial temp of water 23 deg C
    Final temp of water 6 deg C
    Specific Heat Capacity copper 385 J kg-1K-1
    Specific Heat Capacity water 4185 J kg-1K-1
    Specific Latent Heat Fusion of Ice 335 kJ kg-1

    Calculate a value for the Specific Heat Capacity of ice in J kg-1K-1.

    2. Relevant equations

    Q= Mass x Specific Heat Capacity x change in temperature

    3. The attempt at a solution

    I've tried countless attempts and literally spent hours trying to work this out, all have pointed to dead ends and I really don't know what else to try...
    20g = 0.02kg
    335kJ = 335000 J
    105g = 0.105kg

    (0.02kg x 335000J kg-1) + (0.02kg x c) x (6 - -18) = (0.105kg x 4185J kg-1K-1) x (23 - 6)
    6700 + (0.02 x c) x 24 = 439.425 x 17
    6700 + (0.02 x c) x 24 = 7470.225
    0.02 x c x 24 = 770.225
    c = 770.225 / (0.02 x 24)
    c = 1604.635 J kg-1K-1

    Now, I need to work out the SHC of ice which, pre-calculations, we should know it as being around 2000-2100, right? So surely that should mean 1604 is incorrect?
    I've really got no idea what to do anymore, should I have included the SHC of copper and the mass of the calorimeter into the equation somewhere too?
    Any help would be appreciated!
  2. jcsd
  3. Feb 9, 2010 #2
    You have to consider that your system doesn't exchange heat with the universe, or in other words [tex]\delta Q_{U}=0[/tex], so all you have to do now is consider every component in the system that exchanges heat inside the system.

    In a general form it would be something like this:

    [tex]\delta Q_U=\delta Q_{Water}+\delta Q_{Ice} + \delta Q_{Copper}=0[/tex]

    Remember the system is in thermal equilibrium in the final stage, so you can solve it for the variable you need.

    Hope this helps.

    Note: [tex]\delta Q = Q[/tex].
  4. Feb 9, 2010 #3
    Right, I -think- I made some progress
    Assuming the specific heat capacity of copper is calculated to be 536.87
    Q=m x c x delta t
    therefore: Q = 0.0805 x 385 x 17
    Q = 526.87

    Would it then make sense to add this value to the current value of 1604.635
    resulting in 2131.505?
    This would seem to then confirm the assumed value of 2100..?
  5. Feb 9, 2010 #4
    Well what I tried with this problem is:

    Q_ice = -(Q_water + Q_copper)

    Assuming that the copper changes temperature in the same way as the water inside of it, which is a fairly reasonably assumption or the temperatures wouldn't settle in the ways stated, this gives the heat transfer equation as

    (m_ice x dT_ice x C_ice) + ( L_ice x m_ice) + (m_ice x C_water x dT'_ice) = -[(m_water x C_water x dT_water) + (m_copper x C_copper x dT_copper)]

    Plugging in the numbers and rearranging gives me a value of C_ice at 2194 J/kgK.

    P.S. Sorry for the screwy notation. Underscores indicate subscript, d is delta (or change in), m is mass, T is temperature, C is specific heat capacity, L is latent heat of fusion

    EDIT: I forgot to mention, dT_ice is 18 degrees because it goes from -18 to 0 to melt, and dT'_ice is 6 because it then goes from 0 to 6 degrees before reaching equilibrium.
    Last edited: Feb 9, 2010
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