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Heat and Internal Energy - Thermodynamics

  1. Feb 7, 2016 #1
    10g of water at 0˚C added to 100g water at 50˚C

    2. Relevant equations

    3. The attempt at a solution
    So I understand this problem, but I'm not sure when I am supposed to use Q=mL, L being the latency, I think. So with the problem mentioned you can do:

    mw*cw(Tf-0) + mw*cw(Tf-50) = 0 and solve for Tf. Tf= 45.45˚K

    What if I had a problem like
    10g ice at 0˚C added to 100g water at 50˚C? Do you write the equation step by step starting at ice? And do I use Q=mL to account for phase changes only? [solid to liquid] and [liquid to gas]?

    mice*cice(Tf-0) + mL +mw*cw(Tf-50) = 0

    Solve for TF. I think this is set up correctly, but I am not sure. Can you explain the mL part more? Is that the mass of ice * the latency of ice? This is where I get confused on how to do these problems.
  2. jcsd
  3. Feb 7, 2016 #2


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    Staff: Mentor

    Careful with the units there.


    Yes. Starting from ice, you have to convert the water from a solid to a liquid first, and that will require heat.
  4. Feb 7, 2016 #3
    Would you have to do this any time there is a phase change?? No matter what direction, ie liquid to solid or solid to liquid and all the rest. Will the latent heat be given for each phase if there is one?
    Screen Shot 2016-02-07 at 5.48.14 PM.png
  5. Feb 7, 2016 #4


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    Staff Emeritus
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    Homework Helper

    With a substance like water, the values of the latent heat can be looked up.

    Remember, the latent heat of fusion ≠ latent heat of vaporization.
  6. Feb 7, 2016 #5
    Ok, thanks!
  7. Feb 8, 2016 #6


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    Staff: Mentor

    Yes, you have to take into account latent heat for any phase transition. Pay also attention to the sign of the change: for example, when going from solid to liquid, heat enters the substance without any change in temperature, while going from liquid to solid, heat is released from the substance without any change in temperature.

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