HEAT. 686 HEAT. water as the temperature changes is peculiar, inasmuch as it decreases while the temperature increases from 0° to about 4° C, and then it increa.ses as the temperature continues to in- crease. This fact plays a most important part in the economy of nature, as, owing to it, when the temperature at the surface of a pond or lake falls below 4°, the cold water, being lighter, stays on the surface, and ice is formed. Or- dinarily, of course, the colder a liquid is the denser it is: and so, if the surface of a liquid standmg in a tall vessel is cooled, the top i.iyers will sink and the lower ones will rise. There will thus be convection currents until the whole liquid is at the same temperature. Similarly, if the bottom of a vessel of an ordinary liquid is warmed, there will also be convection currents. The motion of these liquid masses is evidently due to the force of gravity, making the denser liquid come below the lighter. The coefficients of cubical expansion at constant pressure are dif- ferent for different liquids and solids ; but for all gases they are practically the same, viz. 0.003662. This most important property of ga.ses is called the 'law of Gay-Lussac,' although its accurate verification is due to Regnault. If Boyle's law is true for a gas. viz. at constant temperature the product of the pressure and volume of a given mass of gas remains constant, it follows at once that the change in pressure of a con- stant volume of a gas as the temperature is raised from 0° to i° obeys the law p = Po( 1+ W, where p„ is the pressure at 0° ; p that at t° ; and /3 is the same coefficient as that for changes in volume, viz. 0.003662. The law that the coeffi- cient of change in pressure at constant volume for all gases is practically the same is some- times called the 'law of Charles.' If both the pressure and temperature of a gas are changed — • assuming Boyle's and Gay-Lussac's laws — it may be shown that under all conditions P (t + 273) is a constant for the gas, where p is the density at t° and pressure p. This may be written m it + 273) where R is a constant for anv one gas, and evi- 1 p dently equals -^77^ — where p„ is the density of the gas at 0° C, and at pressure p. It is evi- dent further from the formula that, if it could he supposed to apply to gases at very low tem- peratures, at t = — 273°, pv ^ 0, an equation which in itself is meaningless. A lower value of / would lead to a negative value for pr. which is absurd. Therefore, the temperature — 273 C. is sometimes called 'absolute zero on the gas scale of temperature:' and / -j- 273, or T as it is written, is called the 'temperature on the abso- lute gas scale.' (A more accurate determination of the coefficient of expansion makes the absolute zero— 273.1° C.) Methods for the measurement of coefficients of expansion are described in all treatises on heat. See Preston, Theory of Heat. Coefficients of Cubical, Expansion 80LIDS Platinum 0.000027 Ci>pper 0.01)0051 Steel 0. 000033 Braes 0.000056 <lla,s8 0.000027 Zinc 0.000087 LIQUIDS Mercury 0.000182 GASES For aU gases 003662 approximately Changes in State. Fusion and Vaporiza- tion. If a tiame is applied to a vessel, such as a glass beaker, in which, there is a block of ice at a low temperature, at first the temperature will rise, but finally a temperature is reached when there is no longer any change and the ice begins to melt. If during the process the mi.xture of ice and water is stirred the temperature will re- main unaltered until all the ice is melted; then the temix!rature will again rise until the water begins to boil, when the temperature is again constant until all the water is boiled away; and then the temperature of the steam will rise. Con- versely, if tlie steam is cooled, it will begin to cond'?nse into water at the same temperature as that at which it boiled, provided its pressure is the same; but so long as it is condensing there is no change in temperature ; then when all is condensed the temperature of the water will fall until it begins to freeze, as it will at the same temperature as that at which the ice melted, jn-ovided the pressure on it is the same; and during the process of freezing there is no change of temperature, but when it is com- pleted there is again a fall. This course of events is common to all crystalline solids; but many solids, such as waxes, liave no definite tem- perature at which they melt, but pass through a pasty condition from solid to liquid, the tem- perature continually rising; and the converse happens when they become solids. There is, then, in the case of ice and similar bodies, a temperature at which the solid and liquid states are in equilibrium together, unless there is ad- dition or withdrawal of heat-energy. This is called the 'fusion-point.' There is also a tempera- ture at which the liquid and the vapor are in equilibrium unless there is addition or with- drawal of heat-energy. This is called the "boil- ing-point.' Both these equilibrium temperatures vary with the pressure on the bodies. As the pressure is increased on a liquid its boiling-point is raised, and conversely, e.g. in the case of water, a change of pressure from 76 to 77 centi- meters of mercury changes the boiling-point from 100° to 100.37°. ■ Fusion and Boiling Points Fusion-point ^""'"'^■PpZ™?* ""^'"^^ Platinum about 1800" C. .Sulphur 444..'; C. Copper " 1096 Merourv 357. Gold " 1092 WatCT 100. Silver " 985 Etlivl alcohol 78. Zinc 415 Ethyl ether 34.6 Bismuth 268 Carbon dioxide -79. Sulphur 115 Ox.vKPu -183. Mercury -39 Nitrop:en —104. Hydrogen —238. As the pressure on most solids is increased, their melting-point is increased also; but there are certain exceptions, viz. those substances which on melting occupy smaller volumes in the liquid than in the solid states. Such solids are ice. cast iron, bismuth. This change in the freezing-point is, however, most minute. In the ease of ice, the melting-point is changed from 0° to — 0.0075° C. if the pressure on the ice is increased from one to two atmospheres. The phenomenon of 'regelation' is due to this last fact. Mien the pressure on a piece of ice is
