1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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 of melting ice cube initially at -5°C

  1. Aug 13, 2014 #1
    1. The problem statement, all variables and given/known data
    Calculate the entropy change of an ice cube of mass 10g, at an initial temperature of -5°C, when it completely melts.

    cice = 2.1 kJkg-1K-1
    Lice-water = 3.34x105 Jkg-1

    2. Relevant equations
    dQ = mcdT
    dS = [itex]\frac{dQ}{T}[/itex]
    ΔS = [itex]\frac{Q}{T}[/itex]
    Q = mL

    3. The attempt at a solution
    First I set the problem out in two stages:
    a) the entropy change from the ice going from -5°C to 0°C (in order to melt)
    b) the entropy change from the ice going to water

    For a)
    dQ = mcdT ---------(1)
    dS = [itex]\frac{dQ}{T}[/itex] ---------(2)

    Putting (1) into (2):

    dS = [itex]\frac{mcdT}{T}[/itex]
    ΔS = mc∫[itex]\frac{1}{T}[/itex]dT
    ΔS = mcln(Tf/Ti)

    ∴ΔS1 = (0.01)(2100)ln([itex]\frac{273}{268}[/itex]) = 0.388 JK-1

    For b)
    Q = mL = (0.01)(3.34x105) = 3340J

    ΔS2 = [itex]\frac{Q}{T}[/itex] = [itex]\frac{3340}{273}[/itex] = 12.23 JK-1

    ∴ total ΔS = ΔS1 + ΔS2 = 0.388 + 12.23 = 12.62 JK-1

    Am I right in simply adding the to changes of entropy together? Does ΔS work like that?

  2. jcsd
  3. Aug 13, 2014 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    Looks good, and the answer is yes, the entropies add. Entropy is a state function, like gravitational potential. If you went from 0 to 1m above ground you would have g x 1m change in potential. If you went from 1m to 2m there would be a further g x 1m change in potential. Giving total change in potential = g x 2m.
  4. Aug 14, 2014 #3
    Great, thanks
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted