These and like instances are sufficient to show us that in general all bodies expand by heat. In order, then, to prepare a reproducible means of measuring temperature, all we have to do is to fix upon a substance (mercury is that most commonly used) by whose changes of volume it is to be measured, and a reproducible temperature, or lather two reproducible temperatures, at which to measure the volume. Those usually selected are —that at which water freezes, or ice melts, and that at which water boils. In both of these cases, the water must be pure, as any addition of foreign matter in general changes the temperature at which freezing or boiling takes place. Another important circum stance is the height of the barometer. See BOILING. The second reproducible tempera ture is therefore defined as that of water boiling in an open vessel when the barometer stands at 30 inches. In absolute strictness, this should also be said of the freezing-point, but the effect on the latter of a change of barometric pressure is practically insensible. The practical construction of a heat-measurer or thermometer on these principles, the various ways of graduating it, and how to convert the readings of one thermometer into those of another, are described in the article TUERMOMETER. In the present article, we suppose the centigrade thermometer to be the one. used, If we make a number of thermometer tubes, fill them with different liquids, and graduate as in the centigrade, we shall find that, though they all give 0' in freezing, and 100° in boiling water, no two in general agree when placed in water between those states. Hence the rate of expansion is not generally uniform for equal increments of heat. It has been found, however, by very delicate experiments, which cannot be more than alluded to here, that mercury expands nearly uniformly for equal increments of temperature. However, what we sought was not an absolute standard, but a reproducible one; and mer cury, in addition to furnishing this, may be assumed also to give us the ratios of different increments of temperature.
We must next look a little more closely into the nature of dilatation by heat. And first, of its measure. A metallic rod of length 1 at 0°, increases at t ° by a quantity which is proportional to t and to 1. Hence k being some numerical quantity, the new length / (1 + 1,1). Here k is called the coefficient of linear dilatation. For instance, a brass rod of length 1 ft. at 0°, becomes at I° (1 + .000018a) ft.; and here k, or the coefficient of linear dilatation for one degree (centigrade), is .0000187; or a brass rod has its length increased by about 53,000th part for each degree of temperature.
If we consider a bar (of brass, for instance) whose length, breadth, and depth are 1, b, d—then, when heated, these increase proportionally. Hence, 1 = 1(1 + kt), b' = b (1 ++ kt), d' = d (1 kt ); and therefore the volume of, or space occupied by. the bar increases from V or tbd to V' or l'b'd'.
Hence V' = V(1 + = V(1 + 3kt) nearly, since k is very small.
Therefore we may write V' = V(1 + Kt), where we shall have as before K, the coeffi cient of cubical dilatation for 1° of temperature. And, as K = 31c, we see that, for the same substance, the coefficient of cubical dilatation is three times that of linear dilatation.
In the following table, these coefficients are increased a hundredfold, as it gives the proportional increase of volume for a rise of temperature from 0° to centigrade. It must also be remarked, that while time linear dilatation of solids is given, it is the cubical dilatation of liquids and gases which is always observed. Moreover, as the latter are
always measured in glass, which itself dilates, the results are only apparent; they are too small, and require correction for the cubical dilatation of glass. This however, is com paratively very small, and may in general be neglected.
Glass 00086I Water .0466 Iron 00122f Alcohol 116 Zinc .00294Air 3665 Mercury 01543I Hydrogen. .... .. .3668 There is one remarkable exception to the law that bodies expand by heat—viz, that of water, under certain circumstances. From 0° (centigrade), at which it melts, it con tracts as the heat is increased, up to about 4° C., after which it begins to expand like other bodies. We cannot here enter into speculations as to the cause of this very singu lar phenomenon, but we will say a few words about its practical utility. Water, then, is densest or he a vie st at 4° C. Hence, in cold weather, as the surface-water of a lake cools to near 4°, it becomes heavier than the hotter water below, and sinks to the bottom. This goes on till the whole lake has the temperature 4°. As the cooling proceeds further, the water becomes lighter, and therefore remains on the surface till it is frozen. Did water not possess this property, a severe winter would freeze a lake to the bottom, and the heat of summer might be insufficient to remelt it all.
Specific thermometer indicates the temperature of a body, but gives us no direct information as to the amount of heat it contains. Yet this is measurable, for we may take as our LNIT the amount of heat required to raise a pound of water from 0° to 1°, which is of course a definite standard. As an instance of the question now raised— Is more heat (and if so, how much more) required to heat a pound of water from zero to 10°, than to twat a pound of mercury between the same limits? We find by experiment that bodies differ extensively in the amount of heat (measured in the units before men tioned) required to produce equal changes of temperature in them.
It is a result of experiment (sufficiently accurate for all ordinary purposes) that if equal weights of water at different temperatures be mixed, the temperature of the mixture will be the arithmetic mean of the original temperatures. From this it follows,with the same degree of approximation, that equal successive amounts of heat are required to raise the same mass of water through successive degrees of temperatures. As an instance, sup pose one pound of water at 50° to be mixed with two pounds at 20°, the resulting tem perature of the mixture is 30°; for the pound at 50° has lost 20°, while each of the other two pounds has gained 10°. Generally, if 9/2, pounds of water at I degrees be mixed with M pounds at 1' degrees (the latter being the colder), and if 0 be the temperature of the mixture—the number of units lost by the first is m(t—O), since one is lost for each pound which cools by one degree; and that gained by the second is M(0—T), and these must be equal. Hence = 1V1(0—T), whence, at once, = rat + MT m+31 ' But if we mix water and mercury at different temperatures, the resulting temperature is found not to agree with the above law. Hence it appears that to raise equal weights of different bodies through the same number of degrees of temperature, requires different amounts of heat. And we may then define the specific heat of a substance as the num ber of units of heat required to raise the temperature of one pound of it by one degree.