How Do You Calculate Entropy Change When Melting Ice at Varying Temperatures?

[chriswilson]

Homework Statement

1. Homework Statement
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 category

 

[gneill]

Homework Statement

1. Homework Statement
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 think your heat capacity units should be J K^-1 mol^-1, and the value for ice should be 38, not 3.8.

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?

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.