Entropy change for melting ice

  1. 1. The problem statement, all variables and given/known data
    1. The problem statement, all variables and given/known data
    Calculate the entropy change when 1 mole of ice at 268 K is melted to form water at 323 K. The heat capacity of ice is 3.8 J K-1 kg-1 and that of water is 75 J K-1 kg-1. The enthalpy of fusion of ice at 273 K is 6.02 kJ mol-1.

    I know the entropy change by the melting of the ice is given by

    delta(S)=delta(Q)/T

    and that this is worked out by the enthalpy of fusion.

    My question is how do I calculate the entropy change caused by the change in temperature since it is not at a constant temperature does this mean the first equation cannot be used?

    Also this isn't a homework question it is an exam question from a previous year and my exam is tomorrow.


    Not sure whether this should be in here or in other sciences catagory
     
  2. jcsd
  3. gneill

    Staff: Mentor

    I think your heat capacity units should be J K-1 mol-1, and the value for ice should be 38, not 3.8.
    For a given molar quantity M of substance with heat capacity constant C, the total heat held by the substance at absolute temperature T is

    Q = M*C*T

    Differentiating:

    dQ = M*C*dT

    So your equation for the change in entropy becomes an integral over the temperature change.
     
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