The change in entropy can be calculated using the equation:

ΔS = Q / T

Where ΔS is the change in entropy, Q is the heat transferred, and T is the temperature. In this case, we are given the latent heat of fusion for water, which is 80 kgm^-1. Let's calculate the change in entropy step by step:

1. Identify the heat transferred:
Since we are given the latent heat of fusion, which is the amount of heat required to convert 1 kg of a substance from a solid to a liquid at its melting point, we can use this value as the heat transferred. In this case, the latent heat of fusion for water is 80 kgm^-1.

2. Identify the temperature:
The temperature at which the phase change occurs is the melting point of water, which is 0 degrees Celsius or 273 Kelvin.

3. Convert the units:
In order to use the equation, we need to make sure the units are consistent. In this case, the latent heat of fusion is given in kgm^-1, but the SI unit for heat is Joules. We can convert the latent heat of fusion to Joules by multiplying it by the mass of the substance involved in the phase change. In this case, we are dealing with 1 kg of water, so the latent heat of fusion in Joules would be 80 Joules.

4. Calculate the change in entropy:
Now that we have the heat transferred (Q = 80 J) and the temperature (T = 273 K), we can plug these values into the equation:
ΔS = 80 J / 273 K
ΔS ≈ 0.293 J/K

Therefore, the change in entropy for the phase change of water from solid to liquid at its melting point is approximately 0.293 J/K.

In summary, the change in entropy for the phase change of water can be calculated using the equation ΔS = Q / T, where Q is the heat transferred and T is the temperature. By substituting the given values, we can determine the change in entropy is approximately 0.293 J/K.