quantity of heat. That branch of the subject that deals with heat measurements is called calorimetry.

218. Thermal capacity. The results of the experiment referred to in section 213, of heating equal masses of iron and water, are often stated by saying that water and iron do not have equal thermal capacities.

There is another simple experiment which shows a difference in thermal capacities of different bodies: Small balls of copper, iron, tin, aluminum, etc., each about 2 centimeters in diameter, are heated in oil to a temperature somewhat above that of boiling water and then dropped on a thin cake of paraffin. The copper and iron balls may melt their way through the wax and fall to the table below, while the others sink to different depths in the wax. The different balls, as judged by the amount of wax they melt, give up different quantities of heat in cooling from the same high temperature down to the temperature of the melting wax. They are said to have different thermal capacities.

The thermal capacity of any body (for example, that of one of the balls just referred to) is equal to the number of calories required to change its temperature 1 degree centigrade. This applies equally to the case of raising and that of lowering the temperature of the body, for the number of calories required to raise the temperature 1 degree is the same as the number of calories given up when the temperature falls 1 degree.

219. Specific heat. The specific heat of any substance is equal to the number of calories required to raise the temperature of 1 gram of the substance 1 degree centigrade. For example, an aluminum vessel has a mass of 500 grams. The specific heat of aluminum is about 0.21 calories per gram per degree. Since the specific heat is the number of calories necessary to raise the temperature of 1 gram of aluminum 1 degree, the number of calories required to raise the entire vessel 1 degree is 500 × 0.21 = 105 calories per degree, which is the thermal capacity.

The thermal capacity of a body is equal to the specific heat of the material multiplied by the mass of the body.

The following expressions will be found useful. The student should think about them until he knows why they are true.

The number of calories required to raise the temperature of a body from t1 to t2 degrees centigrade

= thermal capacity of body × (t2-t1)

= mass of body X specific heat × (t2-t1).

From the definitions of a calorie and of specific heat it should be clear that the specific heat of water is equal to 1.

220. Experimental determination of specific heat. A copper vessel, mass 100 grams, contains 200 grams of water at 15.0° C. A mass of copper, of 300 grams, is heated to a temperature of 100° C. in a steam bath and then suddenly plunged into the vessel of cold water. The final temperature of the mixture is observed to be 24.8° C. From these data the specific heat of the copper can be computed.

Let s be the specific heat of the copper. The copper vessel and the water contained in it are increased in temperature from 15.0° C. to 24.8° C. The number of calories they have gained is 100 s (24.8-15.0) + 200 (24.8 – 15.0). The 300 grams of copper cool from 100° C. to 24.8° C. and lose 300 s (100 – 24.8) calories. The heat received from or given to the room by the vessel and contents during the experiment may be neglected, for the temperature of the vessel was, on the average, probably not far from room temperature. If this is done, we may equate the number of calories gained to those lost, and thus get

100 s (24.8 – 15.0) + 200 (24.8 – 15.0) = 300 s (100 – 24.8). From this

S= 21580

= .091 cal. per gram per degree.

Hence it requires less than one tenth of a calorie to change the temperature of 1 gram of copper 1 degree centigrade. It follows from the definition of a calorie that this is less than the heat required to change the temperature of one tenth of a gram of water 1 degree.

The specific heat of all common solids and liquids is much less than unity, the specific heat of water. The fact that the specific heat of water is relatively so great is the reason why large masses of water have such a moderating effect on climate. Islands surrounded by extensive masses of water do not have the same extremes of temperature as are observed in the interior of a continent. The low winter temperatures and high summer temperatures observed in the central states of the United States are due in large measure to the absence of large bodies of water. Leningrad and London differ in latitude by only a few degrees, yet there is a great difference in their climates, Leningrad being hotter in the summer and much colder in the winter.

221. Summary. It is important to distinguish between temperature and quantity of heat. The modern theory is that heat is a form of energy, and that quantity is the amount of energy that exists in the form of heat.

Three units for the measurement of quantity of heat are used: the calorie, equal to the amount of heat required to change the temperature of 1 gram of water 1 degree centigrade; the kilogram-calorie, equal to the amount of heat required to change the temperature of 1 kilogram of water 1 degree centigrade; the British thermal unit (B.T.U.), equal to the amount of heat required to change the temperature of 1 pound of water 1 degree Fahrenheit.

The thermal capacity of any body is equal to the number of calories required to change its temperature 1 degree centigrade.

The specific heat of a substance is equal to the number of calories required to raise the temperature of 1 gram of the substance 1 degree centigrade. The specific heat of water is larger than that of other common substances. This fact plays an important part in natural phenomena.

PROBLEMS

1. What will be the temperature of 400 gm. of water, initially at 15° C., when 2 kg.-cal. of heat are added?

2. What is the thermal capacity of 250 gm. of water in calories per degree?

3. 500 gm. of water at 15° C. are mixed with 200 gm. at 60° C. Compute the resulting temperature.

4. What is the specific heat of copper if the thermal capacity of a mass of 1.2 kg. is 112 cal. per degree ?

5. 500 gm. of aluminum at 90° C. are mixed with 200 gm. of water at 10° C. What is the resulting temperature if the specific heat of aluminum is 0.21 cal. per gram per degree ?

6. A silver dish of 50 gm. contains 200 gm. of water at 16° C. A piece of silver of 65 gm. is heated to 100° C. and then plunged into the water. What is the resulting temperature? (The specific heat of silver is 0.056 cal. per gram per degree.)

7. A mass of 150 gm. of zinc at 100° C. is dropped into a 60-gram glass beaker (specific heat 0.16 cal. per gram per degree) containing 70 gm. of water at 12° C. The resulting temperature is 25° C. Compute the specific heat of zinc.

8. Into 12 kg. of water at 30° C. are dropped 1 kg. of iron at 100° C. and 1.2 kg. of zinc at 60° C. Find the resulting temperature. (The specific heat of iron is 0.11 cal. and that of zinc 0.092 cal. per gram per degree.) 9. 150 gm. of copper (specific heat 0.093 cal. per gram per degree) was dropped into 400 gm. of water at 10° C. The copper had been heated to a temperature of 99° C. in a water bath. When moved over, it carried with

it 2 gm. of the hot water. Compute the resulting temperature.

CHAPTER XIX

WORK AND HEAT

Reasons for the overthrow of the caloric theory, 222. Joule's experiment, 223. The mechanical equivalent of heat, 224. Examples, 225. Compression and expansion of gases, 226. Adiabatic compression and expansion, 227. Other illustrations of the heating and cooling of gases by compression or expansion, 228. Two important cases; free expansion, 229. Two specific heats of gases, 230. Heats of combustion, 231. Thermodynamics, 232. The first law of thermodynamics, 233. The second law of thermodynamics, 234. Dissipation and degradation of energy, 235. Summary, 236.

222. Reasons for the overthrow of the caloric theory. The reasons for the abandonment of the old caloric theory and the acceptance of the modern theory may be classified into three groups:

1. The concept of a substance like the caloric leads to inconsistencies. If heat is a substance, one would expect that in an isolated group of bodies the total amount of this substance would remain constant. In many cases it does, but in some it does not. For example, in many well-known cases heat is generated by friction. The caloric theory attempted to explain this by saying that the caloric was already in the body, and that the friction rubbed it out. According to this idea there should be less caloric left in a body which had been rubbed. Count Rumford (1753-1814) was one of the first to challenge this. While in charge of the manufacture of cannon at Munich he was greatly impressed by the immense quantity of heat developed in the boring process. Using a blunt drill, he generated large amounts of heat. He even boiled water which had been placed in a surrounding jacket. He argued that if heat were a substance, no body could have the apparently unlimited supply that could be brought out through friction. Another fact worth mentioning is that the shavings or borings have the same specific heat as the solid materials; that is, both the shavings and an equal mass of the solid metal give out the