You are watching: What does the latent heat of fusion measure

In the figure below the ice hasbeen added to the warm water and melted. We are at the "midway"point of the experiment; the ice has turned from a solid to a liquidbut its temperature hasn"t changed, it is still 0oC.

This energy came from the warmwater and cause the water to cool (from Tinitial to Tmid). Wecould use the following equation to determine how much energy was takenfrom the water (we won"t do the calculation because we don"t know whatTmid is).

Heat will continue to flow from thewarm water into the 0o C ice water. Energy will flow until all of the waterhas the same temperature, Tfinal.

Now we will combine all theseparate terms. Energy was removed from the water to first meltthe ice and then to warm the ice water to Tfinal. The toal energylost by the warm water is:
We perform the experiment in aninsulated cup and we assume that all of the energy lost by the warmwater was used to melt ice and warm up the ice water; no energy flowedfrom the cup into the cooler air in the room. We"ll add the 1stand 4th equations above together:
We"ll set the energy lost andenergy used equations equal to each other. This gives us anenergy balance equation that can used to determine LHice:

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The specific heat of water is 1cal/gm oC. You can plug this valuetogether with your measured values for Mwater, Mice, Tinitial andTfinaland solve for LHice. An example calculation using the data shownin the figures above is given below. The known value for thelatent heat of fusion of ice is 80 calories/gram so the measured valuebelow compares pretty well.