outside vessel to protect it from air currents and radiation from external objects. The mass of lead A having been heated to, say, 100° is suddenly plunged into the water and the water stirred till its temperature has risen as high as it will.

The heat given out by the lead in cooling from its initial temperature t' to the final temperature of the water t”, is ms(ť′ —t′′) where m is the mass of the lead and s is its specific heat. So also the heat taken in by the water as it warms from its original temperature t to t" is expressed by WS' (t" -t), where W is the weight of water and S' is its specific heat, which in ordinary work is taken as 1.

But the heat given out by the lead must be equal to that received by the water, therefore

In the above discussion the heat that went into the cup containing the water has been neglected. But clearly the cup must have experienced the same change in temperature as the water that it contains, and so must have received an amount of heat equal to m's' (t"-t), m' and s' representing its mass and specific heat. This heat also came from the lead and so must be added to the right-hand side of the above equation; the result is then

The quantity m's' represents the quantity of heat measured in gram calories required to raise the temperature of the calorimeter cup one degree. It is called the water equivalent of the calorimeter because it represents the number of grams of water that would require as much heat to raise its temperature one degree as the calorimeter cup requires. It will be noticed that the water equivalent of the calorimeter is added directly to the mass of water which it contains. The water equivalent of the stirring rod and thermometer should be included also, as they, too, are raised in temperature by heat coming from the lead.

The form of heater shown in figure 220 was devised by Regnault. The substance to be heated is suspended in the central tube surrounded by the steam jacket. A thermometer with its bulb in a cavity in the middle of the substance serves to show the steady temperature to which it finally comes. The calorimeter is slipped under the heater and the substance lowered into the calorimeter cup without exposure to cold air

currents.

If the substance to be tested is in small fragments they may be held in a basket of light wire gauze whose heat capacity has been previously determined. If the solid is soluble in water some other liquid in which it does not dissolve must be used in the calorimeter. The specific heat of liquids as well as solids may be found in this way, provided there is no chemical action between the liquid and the water in the calorimeter cup which would cause either a development or an absorption of heat.

402. Compensation Calorimeters.-In certain cases, especially where the calorimeter is of necessity large, it is important that the temperature of the instrument may be kept constant so that its heat capacity or water equivalent need not be known.

In the Junkers calorimeter, for instance, used to measure the heat developed in the combustion of gas or oil flames, a stream of cold water flows through a long copper pipe which is coiled around the combustion chamber. When all comes to a steady state the heat removed by the stream of water per second must be just equal to the heat arising from the combustion in the same time. The temperature of the water is measured at the inlet and also at the outlet by delicate thermometers, and the gain in temperature multiplied by the number of grams of water flowing through per minute gives the heat carried away by the stream of water in that time.

403. Electrical Calorimeters.-The specific heats of liquids may be compared by heating first one and then the other in a calorimeter vessel by means of a current of electricity passing through a coil of wire immersed in the liquid. If the heat developed per second by the electric current is just the same in one case as in the other, and if the masses of liquid used in the two cases are such that the temperature rises at exactly the

same rate in both cases, then the heat capacities of the two liquid masses must be the same; that is

=

where m, and m, are the masses of the two liquids and s, and s2 are their respective specific heats.

404. Two Specific Heats of Gases.-The specific heat of a gas may be measured while its pressure is kept constant, or it may be measured when the gas is enclosed in a bulb and kept at constant volume. Experiment shows that the specific heat at constant pressure is greater than the specific heat at constant volume, and when we come to discuss the relation of heat to work we shall find why this is so.

(§414.)

Regnault measured the specific heats of various gases at constant pressure by causing a stream of gas to flow first through a long copper tube coiled in a vessel of hot oil, and then through a copper tube coiled in the calorimeter vessel and surrounded by water. The gas was heated by the oil bath and gave up its heat on passing through the calorimeter so that when the mass of gas which passed through the calorimeter was known its specific heat could be determined.

Great difficulty was found in measuring the specific heat of a gas at constant volume, because its heat capacity is very much less than that of the vessel in which it is enclosed; but the determination was successfully made by Joly using the steam calorimeter (§443).

The relative molecular weights of the gases are given in the fourth column. Evidently 32 grams of oxygen will contain the same number of molecules as 2 grams of hydrogen or 28 grams of nitrogen. The heat capacities of these weights of the various gases is shown in the next column, which indicates that the more perfect gases require nearly the same amount of heat per molecule to raise their temperatures one degree.

In the last column is shown the heat required to raise equal volumes of the different gases one degree in temperature, a volume of 1000 c.c. at 0° C. and at atmospheric pressure being taken in each case. Here again is to be noted the equality of the values for the more perfect gases, as would be expected from Avogadro's law that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

405. Change of Specific Heats with Temperature.-The specific heats of the more perfect gases are nearly constant. The specific heats of solids and liquids are in general greater at high temperatures than at low. In case of most metals the change is small, but carbon, boron, and silicon show marked increase. These substances have been studied by H. F. Weber, who finds in case of diamond at -50° specific heat .0635, while at 985° it is 0.4589, the value changing very rapidly at low temperatures and becoming almost constant above 800°. Also the various forms of carbon, graphite, and diamond differ greatly in their specific heats at low temperatures, but come to nearly the same value as the temperature is raised.

406. Dulong and Petit's Law.-Dulong and Petit in 1819 showed that the product of the specific heats of elements in the solid state by their atomic weights was approximately constant. This constant is proportional to the heat required to raise one atom one degree and is therefore known as the atomic heat. Certain marked exceptions are boron, carbon, and silicon, but all of these substances have specific heats which vary greatly with the temperature, and are marked by particularly high melting points.

The following table shows the atomic heats in case of some substances:

1. If 3 kilograms of copper at 100° placed in 3 kilograms of water

at 10° C. raise the temperature of the water to 17.7° C., find the specific heat of the copper.

2. A mass of 300 grm. of platinum heated to the temperature of a furnace is dropped into 1000 grm. of water and raises its temperature from 15° C. to 25° C. Find the temperature of the furnace, taking. the average specific heat of the platinum as .033.

3. A mass of 150 grm. of copper heated to 100° is dropped into 350 grm. of water at 12° contained in a thin copper vessel weighing 30 grm. Find the resulting temperature, taking the specific heat of copper as .094.

4. How much heat is required to warm the air in a room 3 x 6 x 5 meters in size, from 0° C. to 20° C., the pressure being constant?

5. A mass of 750 grms. of iron at 100° C. is dropped into a copper calorimeter containing 557.8 grm. of water at 15° C. and warms it up to 25° C. Find the specific heat of the iron if the copper vessel weighs 50 grams.