Temperature and States of Matter Help

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


When matter is heated or cooled, it often does things other than simply expanding or contracting, or exerting increased or decreased pressure. Sometimes it undergoes a change of state . This happens when solid ice melts into liquid water or when water boils into vapor, for example.

Thawing And Freezing

Consider our old friend, water. Imagine that it is late winter in a place such as northern Wisconsin and that the temperature of the water ice on the lake is exactly 0°C. The ice is not safe to skate on, as it was in the middle of the winter, because the ice has become “soft.” It is more like slush than ice. It is partly solid and partly liquid. Nevertheless, the temperature of this soft ice is 0°C.

As the temperature continues to rise, the slush gets softer. It becomes proportionately more liquid water and less solid ice. However, its temperature remains at 0°C. Eventually, all the ice melts into liquid. This can take place with astonishing rapidity. You might leave for school one morning and see the lake nearly “socked in” with slush and return in the evening to find it almost entirely thawed. Now you can get the canoe out! But you won’t want to go swimming. The liquid water will stay at 0°C until all the ice is gone. Only then will the temperature begin to rise slowly.

Consider now what happens in the late autumn. The weather, and the water, is growing colder. The water finally drops to 0°C. The surface begins to freeze. The temperature of this new ice is 0°C. Freezing takes place until the whole lake surface is solid ice. The weather keeps growing colder (a lot colder if you live in northern Wisconsin). Once the surface is entirely solid ice, the temperature of the ice begins to fall below 0°C, although it remains at 0°C at the boundary just beneath the surface where solid ice meets liquid water. The layer of ice gets thicker. The ice near the surface can get much colder than 0°C. How much colder depends on various factors, such as the severity of the winter and the amount of snow that happens to fall on top of the ice and insulate it against the bitter chill of the air.

The temperature of water does not follow exactly along with the air temperature when heating or cooling takes place in the vicinity of 0°C. Instead, the water temperature follows a curve something like that shown in Fig. 11-4. In part a , the air temperature is getting warmer; in part b , it is getting colder. The water “stalls” as it thaws or freezes. Other substances exhibit this same property when they thaw or freeze.

Temperature, Pressure, and Changes of State Temperature and States of Matter Heat Of Fusion

Fig. 11-4 . Water as it thaws and freezes, (a) The environmental temperature is getting warmer, and the ice is thawing, (b) The environmental temperature is getting colder, and the liquid water is freezing.

Heat Of Fusion

It takes a certain amount of energy to change a sample of solid matter to its liquid state, assuming that the matter is of the sort that can exist in either of these two states. (Water, glass, most rocks, and most metals fill this bill, but wood does not.) In the case of ice formed from pure water, it takes 80 cal to convert 1 g of ice at 0°C to 1 g of pure liquid water at 0°C. This quantity varies for different substances and is called the heat of fusion for the substance.

In the reverse scenario, if 1 g of pure liquid water at 0°C freezes completely solid and becomes ice at 0°C, it gives up 80 cal of heat. The heat of fusion is thus expressed in calories per gram (cal/g). It also can be expressed in kilocalories per kilogram (kcal/kg) and will yield exactly the same numbers as the cal/g figures for all substances. When the substance is something other than water, then the freezing/melting point of that substance must be substituted for 0°C in the discussion.

Heat of fusion is sometimes expressed in calories per mole (cal/mol) rather than in calories per gram. However, unless it is specifically stated that the units are intended to be expressed in calories per mole, you should assume that they are expressed in calories per gram.

If the heat of fusion (in calories per gram) is symbolized h f , the heat added or given up by a sample of matter (in calories) is h , and the mass of the sample (in grams) is m , then the following formula holds:

h f = h / m

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