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Latent Heat and conservation of energy

  1. Jan 19, 2013 #1
    1. The problem statement, all variables and given/known data
    A cooking vessel on a slow burner contains 11.0 kg of water and an unknown mass of ice in equilibrium at 0°C at time t = 0. The temperature of the mixture is measured at various times. During the first 50.0 min, the mixture remains at 0°C. From 50.0 min to 60.0 min, the temperature increases to 2.00°C. Ignoring the heat capacity of the vessel, determine the initial mass of ice.



    2. Relevant equations

    Q =mcΔT; Q= mL

    cwater=4186
    Lfusion=333000

    Qhot + Qcold=0

    3. The attempt at a solution
    miceLfusin+micecwaterΔT+mwatercwaterΔT = 0

    mice(333000) + mice(8372) + 92092 = 0

    This gives me mice = 0.269kg but i know this is wrong. Any pointers would be greatly appreciated.
     
  2. jcsd
  3. Jan 19, 2013 #2

    CWatters

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    During the melting phase all the energy goes into melting the ice (water stays at zero) so

    Mice * Lfusion = Power * Timemelt

    After melting during the heating phase..

    (Mwater + Mice) * Cwater * ΔT = power * Timeheat

    Two unknowns and two equations.
     
  4. Jan 19, 2013 #3
    Thanks for the reply... I reworked the problem but im still getting it wrong somehow...
     
  5. Jan 19, 2013 #4
    ok now I got it... I mustve been doing something wrong with the calculations...how did you know to bring power into the formula?
     
  6. Jan 19, 2013 #5

    SteamKing

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    What is the definition of power?
     
  7. Jan 19, 2013 #6

    CWatters

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    I started by writing out..

    Mice * Lfusion = Emelt

    but then you get stuck because there isn't enough info in the problem statement to calculate the energy and the timing information hadn't been used.

    Energy is related to power using...

    Power = Energy/time

    or

    Energy = Power * Time.

    I made the reasonable assumption that the heater element delivered constant power.
     
  8. Jan 21, 2013 #7
    ok thank you!
     
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