Calculation of entropy change for melting ice

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To calculate the total entropy change when melting ice at 268 K to water at 323 K, both the entropy change during melting and the change in temperature must be considered. The entropy change from melting can be calculated using the enthalpy of fusion, while the change in temperature requires integrating the heat capacity over the temperature range. Since the process is not at a constant temperature, the integration of heat capacity with respect to temperature is necessary to find the total entropy change. The formula delta(S) = delta(Q)/T applies, but adjustments must be made for varying temperatures. This approach ensures an accurate calculation of the entropy change for the entire process.
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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.
 
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Relate delta(Q) to temperature and integrate.
 

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