CHAPTER VI

SPECIFIC HEAT AND CALORIMETRY

35. Distinction between Temperature and Heat.We now proceed to that branch of our subject which is called calorimetry, and which treats of heat as a measurable quantity. The important difference between temperature and heat may be illustrated by comparing it with the difference between the 'level' or height of a cistern and the quantity of water in that cistern. If two cisterns at different levels are connected by a tube, the water will tend to flow from the higher cistern to the one at a lower level: so in the case of two bodies in thermal communication, heat tends to flow from the one at a higher temperature to the one at a lower temperature. But you cannot

tell from the height of the cistern how much water there is in it, or how much work you could make the water do by turning a wheel. Similarly, the thermometer indicates the temperature of a body, but does not of itself tell us how much heat we can get out of the body.1 You may have a bucketful of hot water and a thimbleful of water equally hot: they are at the same temperature, but it is clear that the bucketful would give out more heat than the thimbleful in cooling through the same number of degrees. And this is equally true of the amounts of heat required to warm them through equal ranges of temperature.

1 Avoid the use of the term 'heat contained in a body.' It is misleading; at any rate it is of no practical importance, for we are only interested in finding how much heat is given out or absorbed by a body when it is cooled or heated, and this obviously depends not only upon its temperature at the time but also upon the temperature to which it is cooled or heated.

36. Heat as a Measurable Quantity.—In measuring lengths we express them in terms of a certain unit of length -the centimetre: we state the mass of a body as being so many grammes-using the gramme as the unit of mass; and so, in order to measure and express quantities of heat, we require to choose a heat-unit, which is defined as follows:-

The unit of heat is the amount of heat required to heat a gramme of water through one degree. This is the same as the amount of heat given out by a gramme of water in cooling through 1o.

It is clear that the amount of heat required to raise the temperature of 2 grammes of water through 1 is twice as great as that required to heat 1 gramme through 1°—or is equal to 2 heat-units to heat 10 grammes through 1° would require 10 units; and so on, the quantity of heat being proportional to the mass of the substance heated.

Again, experiment shows that the amount of heat required to warm a body through a given range of temperature is proportional to that range of temperature, i.e. to the number of degrees through which it is heated. Thus to heat I gramme of water from o° to 100° we require 100 units (the same amount as would be required to heat 100 grammes from o° to 1°). To heat 100 grammes of water from o° to 100° we require 100 X 100 = 10,000 units. A kilogramme (1000 grammes) of water in cooling from 75° to 10° gives out 1000 x 65 = 65,000 units of heat. In general, the amount of heat required to raise m grammes of water through 0° is given by the equation

37. Specific Heat. The question now arises—If we take equal weights of different substances and heat them through equal intervals of temperature, shall we find any differences between the amounts of heat required? The following experiments supply the answer and show that there are such differences.

EXPT. 17.—Apparatus required-A few metal balls or bullets (with hooks attached) made of lead, iron, tin, bismuth, etc.; a cake of beeswax (or a mixture of beeswax and vaseline) about 6 mm. or quarter of an inch thick: this may be made by pouring the melted wax into a flat dish or

by melting the wax on the surface of hot water; bath.

an oil

Suspend the balls from strings, or on a wire support (as in Fig. 21), and heat them to about 150° in the oil-bath. Drop them simultaneously on to the

wax cake. The iron ball melts through first, and is followed by copper, zinc, and tin. Lead is barely able to get through: the bismuth ball will probably not get through at all.

Now the rate at which any ball melts through depends chiefly upon the amount of heat which it gives out in cooling, for this determines how much wax it will melt; it also depends upon the density (Art. 24) of the ball, for the densest ball would tend to sink fastest through the melting wax, as it would if the balls were thrown into treacle. The lead ball is heavier than any of the others: the density of lead is 11.4, while that of iron is 7.2. Although the lead is so much heavier it does not get through nearly as quickly as the iron. We conclude from this that iron in cooling gives out more heat than lead does.

Fig. 21 [1/8].

EXPT. 18.-Place equal quantities (about 400 c.c.) of water in two beakers, and in these immerse the two bulbs of the differential thermometer (Art. 34). Take equal weights (100 grammes) of water and any metal, say lead shot, and put them in separate test-tubes. Plunge the two test-tubes into the same vessel of hot water, and, after keeping them there for 10 minutes, pour the hot lead into the left-hand beaker and the hot water into the other, moving the bulbs of the thermometer slightly so as to stir the contents of the beakers. The index of the differential thermometer will move, showing that the contents of the right-hand beaker have been warmed more than those of the other.

We conclude from this that the water gives out more heat than the lead in cooling through the same interval of temperature,1 and this is found to hold for all other metals. The experiment may be varied by immersing equal weights of different metals in the two beakers: it will be found that similar differences exist among the metals. This is expressed by saying that every substance has a distinct specific heat, and this term is defined as follows:

The specific heat of a substance is the ratio between the amount of heat required to raise a given mass of that substance through a given interval of temperature and the amount of heat required to raise an equal mass of water through the same interval of temperature.

Thus when we say that the specific heat of mercury is or 0.033, we mean that the amount of heat required to raise a given mass of mercury through any interval of temperature is only one-thirtieth of the amount of heat required to raise an equal mass of water through the same interval of temperature ; or that in cooling through the same range of temperature water would evolve thirty times as much heat as an equal mass of mercury.

We have seen (Art. 36) that m 0 units of heat are required to cause a rise of temperature of 0° in m grammes of water (the specific heat of which is unity). For any other substance, the specific heat of which is less than unity and equal to s say, the amount of heat required will be less in the same proportion and will be given by the equation

H = ms 0

(2) which also expresses the amount of heat given out by a body of mass m and specific heat s in cooling through 0°.

The following examples will illustrate the use of this important equation :—

Ex. 1.-How much heat is required to raise the temperature of a kilogramme of mercury (specific heat = 0.033) from 20° to 170°?

Here 0=170° – 20°= 150°, and m=1 kgm.=1000 gm.

... H=ms 0=1000 X 0.033 X 150=4950,

and the amount of heat required is 4950 units.

1 The fact that the hot water really falls through a somewhat smaller range of temperature only makes the experiment more conclusive.

Ex. 2. If 342 units of heat are imparted to 150 grammes of iron (specific heat=0.114) originally at 10°, what will be the final temperature of the iron?

If we suppose the temperature of the iron to be raised through 0°, we know that

Thus the final temperature of the iron will be 10° + 20° = 30°.

38. Methods of Finding Specific Heats.—(1) The Method of Mixtures.-The specific heat of a substance may be found by heating it to a known temperature and dropping it into a weighed quantity of water contained in a suitable vessel (called a calorimeter). The temperature of the water is observed by means of a thermometer before and after dropping in the hot substance, and from the rise of temperature we can calculate the amount of heat gained by the water. This must be exactly equal to the amount of heat given out by the hot body, provided that care is taken to prevent loss or gain of heat from surrounding bodies during the experiment. Having thus found how much heat the substance gives out in cooling through a known interval of temperature, we can easily calculate its specific heat. This method is described more fully below

(Expt. 19).

(2) The Method of Cooling. The specific heat of a substance can also be found by heating it and allowing it to cool; the rate at which it cools is observed and compared with the rate at which water cools under similar conditions. For example, put equal weights of water and turpentine, both at 50°, into two similar glass beakers or thin metal vessels (suspended by strings so as not to be influenced by surrounding bodies), and put a thermometer in each. Note the time taken by each to cool from 50° to 20°; you will find that the water takes more than twice as long as the turpentine. Since the turpentine cools under just the same conditions as the water, the difference must be due to its lower specific heat, which is less than half that of water.

(3) The Method by Fusion of Ice.—The amount of heat given out by a hot body in cooling to o° can also be measured by finding how much ice it is able to melt. This method of