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Latent Heat Of Fusion

  1. Aug 9, 2013 #1

    Zondrina

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    1. The problem statement, all variables and given/known data

    How much heat is required to heat 0.2kg of ice from -20°C to 30°C?

    2. Relevant equations

    Total heat lost or gained : ##Q = mcΔt## where ##Δt## is the change in temperature and c is the heat capacity.

    Latent Heat Fusion : ##Q = mL_f##

    3. The attempt at a solution

    From my understanding, I think I need to break this problem down into states.

    The ice will start melting at 0°C ( since ice is just condensed water ). So the ice must be heated from -20°C to 0°C for it to melt.

    Then we must use Latent Heat to melt the ice.

    Finally we would have to heat the water from 0°C to 30°C.

    So the amount of heat we would need can be expressed by the equation :

    ##Q_T = Q_{Ice} + Q_{Melt} + Q_{Water} = mc_{Ice}Δt_{Ice} + mL_f + mc_{Water}Δt_{Water}##

    Then plugging and chugging I get :

    ##(0.2 kg)(2100 J/kg°C)(0°C + 20°C) + (0.2 kg)(330000 J/kg) + (0.2)(4200 J/kg°C)(30°C - 0°C) = 99600J##

    Therefore 99600J of heat would be required to heat the ice from its original state to a heated state of water.

    Does this look okay?
     
  2. jcsd
  3. Aug 9, 2013 #2

    TSny

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    Looks good!
     
  4. Aug 9, 2013 #3

    Doc Al

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    Yep, looks good to me as well.
     
  5. Aug 9, 2013 #4

    BruceW

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    yep. looks good to me too. Although you have used 2 significant figures in your values, so does it make sense to have 3 significant figures in your answer?

    edit: hehe, everyone seems to have posted a reply near-simultaneously.
     
  6. Aug 9, 2013 #5

    Zondrina

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    You're all so fast lol. Thanks for the confirm guys :).
     
  7. Aug 9, 2013 #6
    "edit: hehe, everyone seems to have posted a reply near-simultaneously. " It's because it was an easy problem :-)
     
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