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Need help with simple cooling problem.

  1. Feb 12, 2015 #1
    I just need someone to confirm my answer so I can be certain that my book has a typo and I am not making a some minuscule mistake that is leading me to the wrong answer.

    A piece of metal is heated to 300 degrees Celsius and then placed in a cooling liquid at 50 degrees Celsius. After 4 minutes, the metal has cooled to 175 degrees Celsius. Find it's temperature after 12 minutes.



    Equation: F(t)= To+ Ce^-kt

    e= Euler's number

    I started out solving for k


    175= 50 + 300e^-k4
    -50 -50

    125=300e^-k4
    /300 /300
    -The Celsius units cancel out-

    125/300=e^-k4
    Ln Ln

    Ln(125/300)= -4k
    /-4 /-4

    k= .21887

    then I plug in the value of k and solve for what temperature the metal will be after 12 minutes have passed.

    F(t)= 50+300e^-.21887*12

    = 71.700

    I end up getting the answer above but the book says the answer is 81.25

    Thanks in advance for your help.
     
  2. jcsd
  3. Feb 12, 2015 #2

    haruspex

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    If you plug t=0 into your first equation, does it give the right initial temperature?
     
  4. Feb 13, 2015 #3
    Wow.. I can't believe I missed that. Thank you.
     
  5. Feb 13, 2015 #4

    haruspex

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    Btw, there's a very quick way to the answer in this case. You're given an initial temperature difference of 250C, and a later difference of 125C, so you know how long it takes for the difference to halve. In a further twice that time, it quarters to 31C.
     
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