1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Specific Heat Problem

  1. Jan 21, 2013 #1
    1. The problem statement, all variables and given/known data

    I have some boiling water that I am adding potatoes to. I am asked to find the final temp after the potatoes have been added to the boiling water.

    Tiw=100C (initial boiling water temp)
    Tip=30C (initial room temp potatoes)
    mp=0.5kg (mass of potatoes)
    mw=1.5L or 1.5kg (mass of water)
    cw=4.2kj/kg*C (specific heat of water)
    cp=3.4kj/kg*C (specific heat of potatoes)

    2. Relevant equations

    [itex]C=\frac{Q}{\Delta T}[/itex]

    Since no heat is assumed to be lost, Qlost=Qgained

    Subscript w is for water and p is potato

    3. The attempt at a solution



    Both objects reach thermal equilibrium therefore Tf is the same.

    After some algebra I end up with:

    [itex]T_f = \frac{(c_w m_w T_iw) - (c_p m_p T_ip)}{(c_w m_w) - (c_p m_p)}[/itex]

    Then plugging in my given values I end up with 125C which is no way correct.

    I am thinking my error might be how I am choosing my Ti/Tf values. I saw an example somewhere which had a couple of the values switched. Which didn't really make sense because as far as I know, it's always Tf-Ti?

    Where am I making my error? If needed I can post my algebra steps. I did them a few times and got the same answer every time...
    Last edited: Jan 21, 2013
  2. jcsd
  3. Jan 21, 2013 #2
    However if I swap the temp values like an example I saw....


    After the algebra I end up with...

    [itex]T_f = \frac{(c_p m_p T_{pi}) + (c_w m_w T_{wi})}{(c_w m_w) + (c_p m_p)}[/itex]

    I get 85.125C. Which is a lot more reasonable.

    If that's the case, why do the temps get represented like that?
  4. Jan 21, 2013 #3


    User Avatar
    Homework Helper

    Tf-Tw<0 and TF-Tp>0. If you say that the water loses a negative amount of heat, it means it gains heat.

    The water loses cwmw(Tw-Tf) heat. The potato gains cpmp(Tf-Tp) heat, and they are equal.

    Or you can say that the heat transferred to a substance is cm(Tf-Ti) which can be either positive or negative and the sum of the transferred amounts of heat is zero, as heat is not lost.

  5. Jan 21, 2013 #4
    So in this case ΔT isn't necessarily Tf-Ti like most Δ's. It's more for interpretation...if that makes sense.

    I get what you are saying. For this problems the final and initial are "swapped" since the water has to lose heat at the end. If I do final - initial, the ΔT is negative and therefore gains heat, which isn't the case.

    Therefore I need to look at what ΔT is doing and set it up from there? Or am I just reaching for a reason why they are swapped and this doesn't make sense?

    Thanks for the reply!
  6. Jan 22, 2013 #5


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Remember the Zeroth Law of Thermodynamics:

    Heat flows from a body with a higher temperature to a body with a lower temperature.
  7. Jan 22, 2013 #6


    User Avatar
    Homework Helper

    You need not think if you add up the terms cm(tf-ti) and make the sum equal to zero.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook