Page:The American Cyclopædia (1879) Volume XV.djvu/339

 STEAM 327 pressure, determined it with great accuracy for a wide range of temperatures and pressures. At 212 it is 966-1 British thermal units per pound. At any other temperature it is 1091 - 7 0*695(T 32) 0-000000103(T 39*l) 3 (Ran- kine), or nearly 1113-940-695 T. The total amount of heat required to raise one pound of water from any given temperature to the temperature of evaporation, and to evaporate it at the latter temperature, or the total heat of evaporation, is often called the total heat of steam. This varies at different temperatures, and is equal to 1091-7 + 0'305 (T-32)-c 2 (T 2 - 32), or 1081-94 + 0-305 T, from 32. It is nearly 1113-94+0-305 T where the initial tem- perature is hypothetically 0. In these ex- pressions, T is the temperature of vaporization, 02 the mean specific heat of water between the ing point and the temperature of the feed rater, and T 2 the latter temperature. Reck- ling from 212, the values of latent and to- " heat become Z=966-1-0-695(T-212), and rith a given temperature t of feed water, Ji' 1178-6 +0-305(T 212), the total heat in latter case being measured from the initial jmperature of the feed water t to that of the 3am forming at T F. For the centigrade scale, these values become 1= 606 -5 0-695 T, andA'=606-5-+0*305 (T 100). The to- tal heat of steam, expressed in foot pounds of lergy, is H=835,000 + 235-5T. A pound of )od coal, used under a good steam boiler, rill evaporate 8 Ibs. of water at a tempera- ture of 320 F., and a pressure of 75 Ibs. per juare inch above the atmosphere, the tem- jrature of the water when entering the boil- being 40. Here the total heat per pound )f water is (H78-6-40) + 0'305(320-212) = LI 71 '54 ; the heat per pound of fuel is 1171-54 x 8'5=:9958-l ; and the equivalent evaporation rom and at 212 is 9958-1 -5-966-1 = 10-31 Ibs. water per pound of coal. The specific heat )f steam under constant pressure is 0*480. constant volume it is 0"365 ; i. e., the mantity of heat per pound required to raise "le temperature of steam, where its expansion just sufficient to ^keep its pressure constant, 0-480 British thermal units ; and, when con- fined within an unchanging space, its pressure ising with its increase of temperature, the leat required per degree is 0-365 units. The thermal unit is the quantity of heat required to raise the temperature of one pound of water one degree at the temperature of maximum density. The value at other temperatures is ractically the same. Steam, when perfectly free from parties of water, is dry, invisible, and in its physical properties similar to other gases. Its density (air=l) is 0*622. In chang- ing in temperature one degree under constant pressure, it absorbs heat equal to 85*77 foot pounds of work. The work of the evapora- tion of a cubic inch of water at 212 is near- ly equal to that of raising a ton one foot. Its coefficient of expansion becomes equal to that of perfect gases at about 18 above the tem- perature due to its pressure, according to Fair- bairn and Tate. Steam expanding while doing work, as in the steam cylinder of an engine, becomes partially condensed. "When expand- ing without doing work it superheats, the dif- ference of total heats at the temperatures of the extremes of pressure becoming observa- ble as sensible heat in the production of this superheating. The elastic force of saturated steam being dependent only upon its tempera- ture, the relation may be expressed by a math- ematical formula. Many such formulas have been proposed, none of which are exact.- The simplest is Tredgold's, =l76f A 75, in which t is the temperature F. and A the number of atmospheres of pressure. This is correct, within two degrees, from one up to above 25 atmospheres of pressure, and is much more nearly accurate at the extremes of that range. In Southern's formula, which has been much usedbyengineers,P=(^ 7 ^) 5 ' 15 +0-l, in which P is the pressure in inches of mercury. These formulas are now seldom employed, as every work upon this subject contains a table of pressures, temperatures, and volumes. "Where great accuracy is required, and no table is at hand, Rankine's formulas, log. P=A ^, and W^p^_K c, may be use(L j n these formulas, P is the pressure, t absolute temperature (461*2 + T F.), and A, B, and are constants : A=8'259 ; log. B=3'436 ; log. 0=5-599; ^=0*00344; a =0*00001 184. The pressure increases with the temperature at a rate which itself also rapidly increases with rise of temperature. The relative volumes of steam and water can be calculated by Pole's 24250 24250 formulas: V= ^- + 65; P=^ ^; and still more accurately by those of Fairbairn and Tate: V= The relative volume or density of steam under varying pressure can be computed by the use of Rankine's formula, ^-,=(^y in which V and P are the volumes in cubic feet, and the pressure reckoned above a vacuum, in pounds per square inch, of one pound of steam at the given pressure, and V is the volume (26-36 cubic feet) of one pound of steam at P', the atmospheric pressure. A cubic inch of water makes about a cubic foot of dry steam. Steam expanding in the cylinder of a steam engine does not follow the law of expansion of permanent gases, nor does the variation of the ratio of pressure to volume follow any law which has yet been exactly expressed mathe- matically. Rankine considers that pressure varies inversely as the y power of the volume, where the steam neither gains nor loses heat, and as the reciprocal of the % power where kept dry by a steam jacket. More exactly,