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Temperature and States of Matter Help (page 2)

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By — McGraw-Hill Professional
Updated on Sep 5, 2011

Heat of Fusion Practice Problem

Problem

Suppose that a certain substance melts and freezes at +400°C. Imagine a block of this material whose mass is 1.535 kg, and it is entirely solid at +400°C. It is subjected to heating, and it melts. Suppose that it takes 142,761 cal of energy to melt the substance entirely into liquid at +400°C. What is the heat of fusion for this material?

Solution

First, we must be sure we have our units in agreement. We are given the mass in kilograms; to convert it to grams, multiply by 1,000. Thus m = 1,535 g. We are given that h = 142,761 cal. Therefore, we can use the preceding formula directly:

h f = 142,761/1535 = 93.00 cal/g

This is rounded off to four significant figures because this is the extent of the accuracy of our input data.

Boiling And Condensing

Let’s return to the stove, where a kettle of water is heating up. The temperature of the water is exactly + 100°C, but it has not yet begun to boil. As heat is continually applied, boiling begins. The water becomes proportionately more vapor and less liquid. However, the temperature remains at + 100°C. Eventually, all the liquid has boiled away, and only vapor is left. Imagine that we have captured all this vapor in an enclosure, and in the process of the water’s boiling away, all the air has been driven out of the enclosure and replaced by water vapor. The stove burner, an electric type, keeps on heating the water even after all of it has boiled into vapor.

At the moment when the last of the liquid vanishes, the temperature of the vapor is + 100°C. Once all the liquid is gone, the vapor can become hotter than + 100°C. The ultimate extent to which the vapor can be heated depends on how powerful the burner is and on how well insulated the enclosure is.

Consider now what happens if we take the enclosure, along with the kettle, off the stove and put it into a refrigerator. The environment, and the water vapor, begins to grow colder. The vapor temperature eventually drops to +100°C. It begins to condense. The temperature of this liquid water is +100°C. Condensation takes place until all the vapor has condensed. (But hardly any of it will condense back in the kettle. What a mess!) We allow a bit of air into the chamber near the end of this experiment to maintain a reasonable pressure inside. The chamber keeps growing colder; once all the vapor has condensed, the temperature of the liquid begins to fall below +100°C.

As is the case with melting and freezing, the temperature of water does not follow exactly along with the air temperature when heating or cooling takes place in the vicinity of +100°C. Instead, the water temperature follows a curve something like that shown in Fig. 11-5. In part a , the air temperature is getting warmer; in part b , it is getting colder. The water temperature “stalls” as it boils or condenses. Other substances exhibit this same property when they boil or condense.

Temperature, Pressure, and Changes of State Temperature and States of Matter Boiling And Condensing

Fig. 11-5 . Water as it boils and condenses, (a) The environmental temperature is getting warmer, and the liquid water is boiling. (b) The environmental temperature is getting colder, and the water vapor is condensing.

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