How to calculate the change in entropy?

Question

Hi. I am wondering how you calculate the change in entropy if the substance is undergoing a phase change. I'm not sure which phase's specific heat to apply to the formula dS= C ln (Tf/Ti)

For example:
What is dS for melting 1.0kg solice ice at 0 C to liquid water at 0 C

or

Vaporizing 1.0 kg of liquid water at 100 C to steam at 100 C

Thank you.

Answer 1

You don't use the formula ΔS = Cp*ln(Tf/Ti) when calculating the change in entropy for an isothermal phase change. You calculate the entropy change for a phase change just like you calculate the entropy change for any other reaction: add up the stoichiometrically weighted entropies of the products and subtract the stoichiometrically weighted sum of the entropies of the reactants. In the case of a simple isochemical phase change, ΔS_reaction = S_product - S_product. The entropies on the right hand side of this equation can be absolute entropies, entropies of formation, or some other relative entropy, so long as the same convention is used for the entropies of both the reactant and product.



If you happen to know the enthalpy of the phase change, and the temperature at which the phase change occurs, then you also know the entropy change. During a phase change, the reactants and products are at equilibrium. That means that ΔG_r of the reaction is zero, so:



ΔG_r = 0 = ΔH_r - T*ΔS_r



so



ΔS_r = ΔH/T



For a melting or vaporization reaction, ΔH_r is the heat of fusion or heat of vaporization, respectively. The entropy change is simply the enthalpy change divided by the thermodynamic temperature at which the reaction occurs.

Answer 2

Calculating Entropy

Answer 3

Change In Entropy Equation

Answer 4

calculate change entropy