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!

Entropy change as water is frozen

  1. May 9, 2015 #1
    1. The problem statement, all variables and given/known data
    A vessel containing 500 g of water, at a starting temperature of 15.0 ◦C, is placed in a freezer at −10.0 ◦C, and left to freeze. (i) If the heat capacity of the vessel is negligible, show that the total entropy change for the system of the water and the inside of the freezer, after the ice reaches the temperature of the inside of the freezer, is 31.4 J K−1 . Is this consistent with the second law of thermodynamics?

    The specific heat capacities of liquid water and ice are 4190 J kg−1 K−1 and 2100 J kg−1 K−1 respectively, and its latent heat of fusion is 3.34 × 105 J kg−1 . Take the melting point of ice to be 273 K.]

    2. Relevant equations

    [tex]\Delta S = mc\ln\frac{T_2}{T_1}[/tex]
    [tex]\Delta S = \dfrac{\Delta Q}{T}[/tex]
    [tex]Q= mc\Delta T[/tex]
    [tex]Q=ml[/tex]

    3. The attempt at a solution

    [tex]\Delta S_{water} = m\left[c_{water}\ln\frac{T_2}{T_1} + \frac{l}{T} + c_{ice}\ln\frac{T_2}{T_1}\right][/tex] = -762.9 J K^{-1}

    [tex]\Delta S_{surroundings} = m\frac{c_{water}\Delta T + l + c_{ice}\Delta T}{T}[/tex] = 751.7 J K^{-1}

    I'm getting an incorrect value. What is wrong with my calculation?
     
    Last edited: May 9, 2015
  2. jcsd
  3. May 9, 2015 #2
    It looks like the equations you wrote are correct. So now show us the details of the calculations.

    Chet
     
  4. May 9, 2015 #3

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    In particular, which numbers do you use where?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted