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Phase change! Melting ice with hot tea.

  1. Oct 19, 2009 #1
    1. The problem statement, all variables and given/known data

    175 cm3 of hot tea at 87°C are poured into a very thin paper cup with 80 g of crushed ice at 0°C. Calculate the final temperature of the "ice tea". (Hint: think about two processes: melting the ice into liquid and, maybe, warming the liquid.)

    2. Relevant equations

    Q=mc(deltaT)
    Q=mL

    3. The attempt at a solution

    First, I calculated the heat loss by the tea:
    Q1=(.0175)(4186)(87)=63731.9J

    Then the heat needed to melt the ice:
    Q2=(0.08)(33.5e4)=26800J

    Heat gain by the melted ice-water
    Q3=(.08)(4186)(87)=29134.6J

    Then Q(final)= Q1-Q2-Q3
    =7797.34J

    Set it equal to the entire system
    7797.34J=(0.255)(4186)(T)

    My answer is 7.3 deg Celsius, which is wrong. I can't seem to find what I did wrong!!!
    Please help! Thanks.
     
    Last edited: Oct 19, 2009
  2. jcsd
  3. Oct 19, 2009 #2

    rl.bhat

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    Homework Helper

    Hi lwaiyipl, welcome to PF.
    Since Q1> Q2, temperature of the tea does not reach zero degree. So rewrite the first and third equation taking θ as the final temperature of the mixture.
     
  4. Oct 19, 2009 #3
    Hey rl.bhat, thanks for the reply. But I still don't quite get it. If I make the final temperature as a variable, θ, then I will get θ=102.437 deg Celsius, which is hotter than the original 87 deg.
    ARRGH, I am pulling my hairs out for this problem!
     
    Last edited: Oct 19, 2009
  5. Oct 19, 2009 #4

    rl.bhat

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    In Q1 temperature will be (87- θ)
    In Q3 temperature will be θ and mass of the mixture will be .......?
     
  6. Oct 19, 2009 #5
    I see that the work I showed at the first post is incorrect, it's 0.175 instead of 0.0175.
    So
    Q1=(0.175)(4186)(87-θ)

    Q2=(0.08)(33.5e4)

    Q3=(0.175+0.08)(4186)(θ-0)

    Am I setting it up correctly?
    I have a question about Q3, why do we add the tea with the melted ice-water? Aren't we calculating for the amount of heat needed to raise the melted ice-water from 0 deg to θ?
     
  7. Oct 19, 2009 #6

    rl.bhat

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    Yes. You are right.
     
  8. Oct 21, 2009 #7
    Thanks rl.bhat. Sorry about late reply. I got the answer now!
     
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