CHAPTER FIFTH. THERMAL. SECTION XXXIX.-TEMPERATURE. ART. 172.-General Unit. The temperature of a body is its thermal state considered with reference to its power of communicating heat to other bodies. Any unit of difference of temperature may be denoted by ✪. For a ART. 173.-Standard Difference and Derived Units. standard difference of temperature Newton chose the difference between the thermal state of pure water when freezing and the thermal state of the same substance when boiling under the standard atmospheric pressure. While there is unanimity in the choice of a standard, there is diversity in the mode of deriving a unit. The degree of Fahrenheit is the one hundred and eightieth part of the standard interval, while the degree of Celsius is the one hundredth part, and is called on that account the Centigrade degree. The degree of Réaumur is the eightieth part of the same interval. following equivalences, Hence the 9 degs. Fahr. 5 degs. Cent. = 4 degs. Réaumur. = ART. 174.-Scales of Temperature. As temperature is an ordinal quantity it is necessary to fix upon an origin from which to reckon, especially as the state of no temperature cannot be directly observed. Fahrenheit chose for origin the temperature which is 32 of his degrees below the freezing point of water; Celsius and Réaumur chose the lower fixed point, namely, the freezing point of water. In Fig. 24 the three scales are compared, the Fahrenheit directly with the two 80 others. By the following rule a numerical comparative scale of the Centigrade and Fahrenheit degrees can be easily drawn out. On the Centigrade scale O is identical with 32 on the Fahrenheit; for every 5 added to the 0 add a 9 to the 32. For the absolute zero of temperature see Art. 199. Observe that the expression n° F. is used to denote a temperature ; while the expression n deg. Fahr. is used to denote a number of units of temperature. The former quantity is ordinal, the latter is not. ART. 175.-Use of Scales. The Centigrade scale has been generally adopted where the metric system has been adopted. It is commonly used along with the C.G.S. system. The Fahrenheit scale is very generally used in English-speaking countries for purposes of ordinary life, and also for those of science, though the Centigrade scale is com Centigrade Fahrenheit Reaumur ing into use among those who wish their results to be readily followed by foreigners. That of Réaumur is used to some extent on the Continent of Europe for medical and domestic purposes. EXAMPLES. Ex. 1. The point of maximum density of water is 4° Centigrade. What is the same point denoted by on the Fahrenheit scale ? First, to convert the 4 Cent. degrees into Fahr. degrees. 180 deg. Fahr. 100 deg. Cent, Second, to find the ordinal number. The number is 7.2 degs. Fahr. above the freezing point, which is 32 degs. Fahr. above the zero of the Fahrenheit scale; therefore it is 7·2+32° F., i..., 39°.2 F. Ex. 2. Express on the Centigrade scale 85° F., 0° F., -20° F. We could proceed as above, first converting the degrees Fahrenheit into degrees Centigrade, and then subtracting the 32 degrees Fahrenheit previously reduced to degrees Centigrade. But it is more expeditious to subtract the 32 from the given number, and then convert the algebraic remainder, the result being the ordinal number required. EXERCISE XXXIX. 1. Convert 212 degrees Fahrenheit into degrees Centigrade; and 100 degrees Centigrade into degrees Fahrenheit. 2. Express 300° C. and 200° C. in terms of the Fahrenheit scale. 3. Express 500° F., 400° F., 300° F., 200° F., 100° F., in terms of the Centigrade scale. 4. Express the British standard temperature of 62° F. in terms of the Centigrade scale, and the French standard temperature of 3° 94 C. in terms of the Fahrenheit scale. 5. Express 327° F., 86° F., 70° F., and 30° F. in terms of the Centigrade scale. 6. Express on the Centigrade scale the following melting points : 7. Express on the Fahrenheit scale the following boiling points : Alcohol, Ether, 8. The following melting points are expressed on the Centigrade scale, express them on the Fahrenheit scale : Mercury, - 39° 44. Tin, 235°. 1500°. 9. The point at which mercury freezes is indicated approximately by the same number on the Fahrenheit and Centigrade scales. Find the number. 10. At what point are the numbers on the scales of Fahrenheit and Réaumur identical? 11. Find the first four coincidences above the freezing point of the Fahrenheit and Centigrade degree divisions. 12. What temperature is denoted on the Fahrenheit scale by double the number it is denoted by on the Centigrade scale? SECTION XL.-HEAT. ART. 176.-General Unit.-Heat, being a species of energy, can be measured in terms of the unit of erergy, for example, by the foot-pound, or the erg, or the joule (Art. 226). But for certain purposes it is found more convenient to define an independent thermal unit, which can afterwards be compared with the unit. of energy. Any unit of heat is denoted by H. ART. 177.-Thermal Unit. The thermal unit is commonly defined by the effect of heat in altering the temperature of a standard substance, when the whole of the heat communicated goes to produce alteration of temperature. The substance chosen is pure water about the temperature of its maximum density, that is, 4° C. The amount of heat required to be communicated to a mass of water to change its temperature from the mth to the nth — is strictly proportional to the mass of the water, but it is not strictly proportional to the difference of temperature n-me. It depends upon the particular values of m and n, and is strictly proportional to the difference of temperature only when the difference is small. This is expressed by saying that the value k of the equivalence depends upon the initial or average temperature of the change. The variation in the value of this equivalence is slight for the range between 0° C. and 4° C.; consequently the unit of heat may be defined by on the understanding that for exact purposes the change is limited to the interval mentioned. ART. 178.-Special Thermal Units. Different units of heat are obtained according to the special units of mass and of temperature adopted. Some of these have no special name, and in consequence are specified by the quantities on which they depend. We have the pound of water by degree Fahrenheit, which is the ordinary British unit; the pound of water by degree Centigrade; the kilogramme of water by degree Centigrade, which is the ordinary French unit; the gramme of water by degree Centigrade. The third of these units is denominated the calorie, and the fourth is denominated the small calorie. ART. 179.-Dynamical Equivalent of Heat. By the mechanical, or, more appropriately, the dynamical equivalent of heat is meant |