FACTORS FOR REDUCTION TO DULONG'S LAW OF RADIATION.

Differences in Temperature between Radiating Body and the Air.

Deg. Fahr.

18

36

54

72

90

108

126

144

162

180

198

216

234

252

270

288

306

324

342

360

378

396

414

432

Temperature of the Air on the Fahrenheit Scale.

104°

32° 50° 59° 68° 86° 104° 122° 140° 158° 176° 194° 212°

1.00 1.07 1.121.16 1.25 1.36 1.47 1.58 1.70 1.85 1.09 2.15 1.03 1.08 1.16 1.21 1.30 1.401.52 1.68 1.76 1.91 2.06 2.23 1.07 1.16 1.20 1.25 1.35 1.45 1.58 1.70 1.83 1.99 2.142.31 1.12 1.20 1.25 1.30 1.40 1.52 1.64 1.76 1.90 2.07 2.232.40 1.16 1.25 1.31 1.36 1.46 1.58 1.71 1.84 1.98 2.15 2.33 2.51 1.211.31 1.36 1.42 1.52 1.65 1.78 1.92 2.07 2.28 2.42 2.62 1.26 1.36 1.42 1.48 1.50 1.72 1.86 2.00 2.16 2.34 2.52 2.72 1.321.42 1.48 1.54 1.65 1.79 1.94 2.08 2.24 2.44 2.64 2.83 1.37 1.48 1.54 1.60 1.73 1.86 2.02 2.17 2.34 2.54 2.74 2.96 1.44 1.55 1.61 1.68 1.81 1.95 2.11 2.27 2.46 2.66 2.87 3.10 1.50 1.62 1.69 1.75 1.89 2.04 2.212.38 2.56 2.78 3.00 3.24 1.58 1.69 1.76 1.83 1.97 2.132.322.48 2.68 2.91 3.13 3.38 1.64 1.77 1.84 1.90 2.06 2.28 2.43 2.52 2.80 3.03 3.28 3.46 1.71 1.85 1.922.00 2.15 2.33 2.52 2.71 2.92 3.18 3.433.70 1.79 1.93 2.01 2.09 2.222.44 2.64 2.84 3.06 3.32 3.58 3.87 1.89 2.03 2.12 2.202.37 2.56 2.782.99 3.223.50 3.77 4.07 1.98 2.13 2.222.31 2.49 2.69 2.90 3.123.373.66 3.95 4.26 2.07 2.232.33 2.42 2.62 2.813.043.28 3.53 3.84 4.14 4.46 2.17 2.34 2.44 2.54 2.73 2.95 3.193.44 3.70 4.024.34 4.68 2.27 2.45 2.56 2.66 2.86 3.09 3.35 3.60 3.88 4.224.55 4.91 2.39 2.57 2.68 2.79 3.00 3.243.51 3.78 4.084.42 4.77 5.15 2.50 2.70 2.81 2.93 3.15 3.40 3.68 3.97 4.28 4.645.01 5.40 2.63 2.84 2.95 3.07 3.31 3.51 3.87 4.124.484.875.265.67 2.76 2.98 3.10 3.23 3.473.76 4.10 4.32 4.61 5.125.33 6.04

The loss of heat by convection appears to be independent of the nature of the surface, that is, it is the same for iron, stone, wood, and other materials. It is different for bodies of different shape, however, and it varies with the position of the body. Thus a vertical steam-pipe will not lose so much heat by convection as a horizontal one will; for the air heated at the lower part of the vertical pipe will rise along the surface of the pipe, protecting it to some extent from the chilling action of the surrounding cooler air. For a similar reason the shape of a body has an important influence on the result, those bodies losing most heat whose forms are such as to allow the cool air free access to every part of their surface. The following table from Box gives the number of heat units that horizontal cylinders or pipes lose by convection per square foot of surface per hour, for one degree difference in temperature between the pipe and the air.

HEAT UNITS LOST BY CONVECTION FROM HORIZONTAL PIPES, PER SQUARE
FOOT OF SURFACE PER HOUR, FOR A TEMPERATURE
DIFFERENCE OF 1° FAHR.

The loss of heat by convection is nearly proportional to the difference in temperature between the hot body and the air; but the experiments of

Dulong and Péclet show that this is not exactly true, and we may here also resort to a table of factors for correcting the results obtained by simple proportion.

FACTORS FOR REDUCTION TO DULONG'S LAW OF CONVECTION.

EXAMPLE IN THE USE OF THE TABLES.-Required the total loss of heat by both radiation and convection, per foot of length of a steam-pipe 2 11/32 in. external diameter, steam pressure 60 lbs., temperature of the air in the room 68° Fahr.

Temperature corresponding to 60 lbs. equals 307°; temperature difference 30768 = 239°.

Area of one foot length of steam-pipe = 2 11/32 × 3.1416 ÷ 12 = 0.614 sq. ft.

Heat radiated per hour per square foot per degree of difference, from table, 0.64. Radiation loss per hour by Newton's law 239° x .614 ft. x .64 = 93.9 heat units. Same reduced to conform with Dulong's law of radiation: factor from table for temperature difference of 239° and temperature of air 68° 1.93. 93.9 X 1.93 181.2 heat units, total loss by radiation.

=

Convection loss per square foot per hour from a 2 11/32-inch pipe: by interpolation from table, 2" = .728, 3′′ = .626, 2 11/32" = .693.

Area, 614 X .693 X 239° 101.7 heat units. Same reduced to conform with Dulong's law of convection: 101.7 x 1.73 (from table) = 175.9 heat units per hour. Total loss by radiation and convection = 181.2175.9 = 357.1 heat units per hour. Loss per degree of difference of temperature per linear foot of pipe per hour =357.1239 1.494 heat units = 2.433 per sq. ft.

It is not claimed, says The Locomotive, that the results obtained by this method of calculation are strictly accurate. The experimental data are not sufficient to allow us to compute the heat-loss from steam-pipes with any great degree of refinement; yet it is believed that the results obtained as indicated above will be sufficiently near the truth for most purposes. An experiment by Prof. Ordway, in a pipe 2 11/32 in. diam. under the above conditions (Trans. A. S. M. E., v. 73), showed a condensation of steam of 181 grammes per hour, which is equivalent to a loss of heat of 358.7 heat units per hour, or within half of one per cent of that given by the above calculation.

According to different authorities, the quantity of heat given off by steam and hot-water radiators in ordinary practice of heating of buildings by direct radiation varies from 1.8 to about 3 heat units per hour per square foot per degree of difference of temperature.

The lowest figure is calculated from the following statement by Robert Briggs in his paper on "American Practice in Warming Buildings by Steam" (Proc. Inst. C. E., 1882, vol. lxxi): "Each 100 sq. ft. of radiating surface will give off 3 Fahr. heat units per minute for each degree F. of difference in temperature between the radiating surface and the air in which it is exposed."

The figure 2 1/2 heat units is given by the Nason Manufacturing Company in their catalogue, and 2 to 2 1/4 are given by many recent writers. For the ordinary temperature difference in low-pressure steam-heating,

say 212°

70° = 142° F., 1 lb. steam condensed from 212° to water at the

same temperature gives up 965.7 heat units. A loss of 2 heat units per sq. ft. per hour per degree of difference, under these conditions, is equivalent to 2 x 142965 = 0.3 lbs. of steam condensed per hour per sq. ft. of heating surface. (See also Heating and Ventilation.)

Transmission of Heat through Walls, etc., of Buildings (Nason Manufacturing Co.). (See also Heating and Ventilation.)-Heat has the remarkable property of passing through moderate thicknesses of air and gases without appreciable loss, so that air is not warmed by radiant heat, but by contact with surfaces that have absorbed the radiation.

POWERS OF DIFFERENT SUBSTANCES FOR TRANSMITTING HEAT.

A square foot of glass will cool 1.279 cubic feet of air from the temperature inside to that outside per minute, and outside wall surface is generally estimated at one fifth of the rate of glass in cooling effect.

Box, in his "Practical Treatise on Heat," gives a table of the conducting powers of materials prepared from the experiments of Péclet. It gives the quantity of heat in units transmitted per square foot per hour by a plate 1 inch in thickness, the two surfaces differing in temperature 1 degree:

Hood, in his "Warming and Ventilating of Buildings," p. 249, gives the results of M. Depretz, which, placing the conducting power of marble at 1.00, give .483 as the value for firebrick.

THERMODYNAMICS.

Thermodynamics, the science of heat considered as a form of energy, is useful in advanced studies of the theory of steam, gas, and air engines, refrigerating machines, compressed air, etc. The method of treatment adopted by the standard writers is severely mathematical, involving constant application of the calculus. The student will find the subject thorougly treated in the recent works by Rontgen (Dubois's translation), Wood, and Peabody.

First Law of Thermodynamics.-Heat and mechanical energy are mutually convertible in the ratio of about 778 foot-pounds for the British thermal unit. (Wood.) Heat is the living force or vis viva due to certain molecular motions of the molecules of bodies, and this living force may be stated or measured in units of heat or in foot-pounds, a unit of heat in British measures being equivalent to 772 [778] foot-pounds. (Trowbridge, Trans. A. S. M. E., vii. 727.)

Second Law of Thermodynamics.-The second law has by different writers been stated in a variety of ways, and apparently with ideas so diverse as not to cover a common principle. (Wood, Therm., p. 389.) It is impossible for a self-acting machine, unaided by any external agency to convert heat from one body to another at a higher temperature. (Clausius.)

If all the heat absorbed be at one temperature, and that rejected be at one lower temperature, then will the heat which is transmuted into work be to the entire heat absorbed in the same ratio as the difference between the absolute temperature of the source and refrigerator is to the absolute temperature of the source. In other words, the second law is an expression for the efficiency of the perfect elementary engine. (Wood.)

=

The living force, or vis viva, of a body (called heat) is always proportional to the absolute temperature of the body. (Trowbridge.) Q Q2 T1 - T2 The expression may be called the symbolical or alQ1 gebraic enunciation of the second law,-the law which limits the efficiency of heat engines, and which does not depend on the nature of the working medium employed. (Trowbridge.) Q and T1 = quantity and absolute

Ti

temperature of the heat received, Q2 and T, = quantity and absolute temperature of the heat rejected.

The expression represents the efficiency of a perfect heat engine which receives all its heat at the absolute temperature T1, and rejects heat at the temperature T2, converting into work the difference between the quantity received and rejected.

EXAMPLE.-What is the efficiency of a perfect heat engine which receives heat at 388° F. (the temperature of steam of 200 lbs. gauge pressure) and rejects heat at 100° F. (temperature of a condenser, pressure 1 lb. above vacuum).

In the actual engine this efficiency can never be attained, for the difference between the quantity of heat received into the cylinder and that rejected into the condenser is not all converted into work, much of it being lost by radiation, leakage, etc. In the steam engine the phenomenon of cylinder condensation also tends to reduce the efficiency.

PHYSICAL PROPERTIES OF GASES.

(Additional matter on this subject will be found under Heat, Air, Gas, and Steam.)

When a mass of gas is enclosed in a vessel it exerts a pressure against the walls. This pressure is uniform on every square inch of the surface of the vessel; also, at any point in the fluid mass the pressure is the same in every direction.

In small vessels containining gases the increase of pressure due to weight may be neglected, since all gases are very light; but where liquids are concerned, the increase in pressure due to their weight must always be taken

into account.

Expansion of Gases, Marriotte's Law. The volume of a gas diminishes in the same ratio as the pressure upon it is increased.

This law is by experiment found to be very nearly true for all gases, and is known as Boyle's or Mariotte's law.

If p = pressure at a volume v, and p1 = pressure at a volume v1, P1V1 = pv; P1 = P; pv = a constant.

v

The constant, C, varies with the temperature, everything else remaining the same.

Air compressed by a pressure of seventy-five atmospheres has a volume about 2% less than that computed from Boyle's law, but this is the greatest divergence that is found below 160 atmospheres pressure.

Law of Charles.-The volume of a perfect gas at a constant pressure is proportional to its absolute temperature. If v be the volume of a gas at 32° F., and v1 the volume at any other temperature, f1, then

v1 = vo (t1 +159.2);

or

491.2

[1 +0.002036(t1 — 32°)]v。.

If the pressure also change from po to p1,

The Densities of the elementary gases are simply proportional to their atomic weights. The density of a compound gas, referred to hydrogen as 1, is one-half its molecular weight; thus the relative density of CO2 is (12+32) = 22.

Avogadro's Law.-Equal volumes of all gases, under the same conditions of temperature and pressure, contain the same number of molecules. To find the weight of a gas in pounds per cubic foot at 32° F., multiply half the molecular weight of the gas by .00559. Thus 1 cu. ft. marsh-gas, CH,

= (124) X .00559 = .0447 lb.

When a certain volume of hydrogen combines with one half its volume of oxygen, there is produced an amount of water vapor which will occupy the same volume as that which was occupied by the hydrogen gas when at the same temperature and pressure.

Saturation-point of Vapors.-A vapor that is not near the saturation-point behaves like a gas under changes of temperature and pressure; but if it is sufficiently compressed or cooled, it reaches a point where it begins to condense: it then no longer obeys the same laws as a gas, but its pressure cannot be increased by diminishing the size of the vessel containing it, but remains constant, except when the temperature is changed. The only gas that can prevent a liquid evaporating seems to be its own vapor. Dalton's Law of Gaseous Pressures.-Every portion of a mass of gas inclosed in a vessel contributes to the pressure against the sides of the vessel the same amount that it would have exerted by itself had no other gas been present.

Mixtures of Vapors and Gases.-The pressure exerted against the interior of a vessel by a given quantity of a perfect gas enclosed in it is the sum of the pressures which any number of parts into which such quantity might be divided would exert separately, if each were enclosed in a vessel of the same bulk alone, at the same temperature. Although this law is not exactly true for any actual gas, it is very nearly true for many. Thus if 0.080728 lb. of air at 32° F., being enclosed in a vessel of one cubic foot capacity, exerts a pressure of one atmosphere or 14.7 pounds, on each square inch of the interior of the vessel, then will each additional 0.080728 lb. of air which is enclosed, at 32°, in the same vessel, produce very nearly an additional atmosphere of pressure. The same law is applicable to mixtures of gases of different kinds. For example, 0,12344 lb. of carbonic-acid gas, at 32°, being enclosed in a vessel of one cubic foot in capacity, exerts a pressure of one atmosphere; consequently, if 0.080728 lb. of air and 0.12344 lb. of carbonic acid, mixed, be enclosed at the temperature of 32°, in a vessel of one cubic foot of capacity, the mixture will exert a pressure of two atmos pheres. As a second example: Let 0.080728 lb. of air, at 212°, be enclosed in a vessel of one cubic foot; it will exert a pressure of

Let 0.03797 lb. of steam, at 212°, be enclosed in a vessel of one cubic foot; it will exert a pressure of one atmosphere. Consequently, if 0.080728 lb. of air and 0.03797 lb. of steam be mixed and enclosed together, at 212°, in a vessel of one cubic foot, the mixture will exert a pressure of 2.366 atmospheres. It is a common but erroneous practice, in elementary books on physics, to de.. scribe this law as constituting a difference between mixed and homogeneous gases; whereas it is obvious that for mixed and homogeneous gases the law of pressure is exactly the same, viz., that the pressure of the whole of a gaseous mass is the sum of the pressures of all its parts This is one of the laws of mixture of gases and vapors.

A second law is that the presence of a foreign gaseous substance in con tact with the surface of a solid or liquid does not affect the density of the vapor of that solid or liquid unless there is a tendency to chemical com bination between the two substances. in which case the density of the vapor is slightly increased. (Rankine, S. E., p. 239.)

Flow of Gases.-By the principle of the conservation of energy, it may be shown that the velocity with which a gas under pressure will escape into a vacuum is inversely proportional to the square root of its density; that is, oxygen, which is sixteen times as heavy as hydrogen, would, under exactly the same circumstances, escape through an opening only one fourth as fast as the latter gas.

Absorption of Gases by Liquids.-Many gases are readily absorbed by water. Other liquids also possess this power in a greater or less degree. Water will for example, absorb its own volume of carbonic-acid gas, 430 times its volume of ammonia, 2 times its volume of chlorine, and only about 1/20 of its volume of oxygen.

The weight of gas that is absorbed by a given volume of liquid is proportional to the pressure. But as the volume of a mass of gas is less as the pressure is greater, the volume which a given amount of liquid can absorb at a certain temperature will be constant, whatever the pressure. Water, for example, can absorb its own volume of carbonic-acid gas at atmospheric pressure; it will also dissolve its own volume if the pressure is twice as great, but in that case the gas will be twice as dense, and consequently twice the weight of gas is dissolved.