Entropy change for melting ice

In summary, the conversation discusses how to calculate the entropy change when melting ice at different temperatures, taking into account the heat capacity and enthalpy of fusion. It is clarified that the heat capacity units should be corrected and an integral is needed to account for the change in temperature.
  • #1

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
 
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  • #2
chriswilson said:

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.
 

What is entropy change for melting ice?

The entropy change for melting ice is the measure of the amount of disorder or randomness that occurs when solid ice changes into liquid water at a constant temperature and pressure.

How is entropy change for melting ice calculated?

The entropy change for melting ice can be calculated using the equation ΔS = Q/T, where ΔS is the change in entropy, Q is the heat absorbed by the ice, and T is the temperature at which the ice melts.

What factors affect the entropy change for melting ice?

The main factors that affect the entropy change for melting ice are temperature, pressure, and the presence of impurities in the ice. Higher temperatures and pressures lead to a greater increase in entropy, while impurities can decrease the entropy change.

Why is the entropy change for melting ice important?

The entropy change for melting ice is important because it is a key aspect of thermodynamics and helps us understand how energy is transferred and transformed. It also has practical applications, such as in refrigeration and food preservation.

How does the entropy change for melting ice relate to the second law of thermodynamics?

The entropy change for melting ice is directly related to the second law of thermodynamics, which states that the entropy of a closed system will tend to increase over time. This means that the entropy change for melting ice will always be positive, as the ice melts and becomes more disordered.

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