The specific heat of a mixture of gases is obtained by multiplying the specific heat of each const.i.tuent gas by the percentage by weight of that gas in the mixture, and dividing the sum of the products by 100.
The specific heat of a gas whose composition by weight is CO_{2}, 13 per cent; CO, 0.4 per cent; O, 8 per cent; N, 78.6 per cent, is found as follows:
CO_{2} : 13 0.217 = 2.821 CO : 0.4 0.2479 = 0.09916 O : 8 0.2175 = 1.74000 N : 78.6 0.2438 = 19.16268 -------- 100.0 23.82284
and 23.8228 100 = 0.238 = specific heat of the gas.
The specific heats of various solids, liquids and gases are given in Table 4.
Sensible Heat--The heat utilized in raising the temperature of a body, as that in raising the temperature of water from 32 degrees up to the boiling point, is termed sensible heat. In the case of water, the sensible heat required to raise its temperature from the freezing point to the boiling point corresponding to the pressure under which ebullition occurs, is termed the heat of the liquid.
Latent Heat--Latent heat is the heat which apparently disappears in producing some change in the condition of a body without increasing its temperature If heat be added to ice at freezing temperature, the ice will melt but its temperature will not be raised. The heat so utilized in changing the condition of the ice is the latent heat and in this particular case is known as the latent heat of fusion. If heat be added to water at 212 degrees under atmospheric pressure, the water will not become hotter but will be evaporated into steam, the temperature of which will also be 212 degrees. The heat so utilized is called the latent heat of evaporation and is the heat which apparently disappears in causing the substance to pa.s.s from a liquid to a gaseous state.
TABLE 4
SPECIFIC HEATS OF VARIOUS SUBSTANCES +--------------------------------------------------------------------+ | SOLIDS | +-------------------------------+----------------+-------------------+ | | Temperature[2]| | | | Degrees | Specific | | | Fahrenheit | Heat | +-------------------------------+----------------+-------------------+ | Copper | 59-460 | .0951 | | Gold | 32-212 | .0316 | | Wrought Iron | 59-212 | .1152 | | Cast Iron | 68-212 | .1189 | | Steel (soft) | 68-208 | .1175 | | Steel (hard) | 68-208 | .1165 | | Zinc | 32-212 | .0935 | | Bra.s.s (yellow) | 32 | .0883 | | Gla.s.s (normal ther. 16^{III}) | 66-212 | .1988 | | Lead | 59 | .0299 | | Platinum | 32-212 | .0323 | | Silver | 32-212 | .0559 | | Tin | -105-64 | .0518 | | Ice | | .5040 | | Sulphur (newly fused) | | .2025 | +-------------------------------+----------------+-------------------+ | LIQUIDS | +-------------------------------+----------------+-------------------+ | | Temperature[2]| | | | Degrees | Specific | | | Fahrenheit | Heat | +-------------------------------+----------------+-------------------+ | Water[3] | 59 | 1.0000 | | Alcohol | 32 | .5475 | | | 176 | .7694 | | Mercury | 32 | .03346 | | Benzol | 50 | .4066 | | | 122 | .4502 | | Glycerine | 59-102 | .576 | | Lead (Melted) | to 360 | .0410 | | Sulphur (melted) | 246-297 | .2350 | | Tin (melted) | | .0637 | | Sea Water (sp. gr. 1.0043) | 64 | .980 | | Sea Water (sp. gr. 1.0463) | 64 | .903 | | Oil of Turpentine | 32 | .411 | | Petroleum | 64-210 | .498 | | Sulphuric Acid | 68-133 | .3363 | +-------------------------------+----------------+-------------------+ | GASES | +--------------------------+---------------+--------------+----------+ | | | Specific | Specific | | | Temperature[2]| Heat at | Heat at | | | Degrees | Constant | Constant | | | Fahrenheit | Pressure | Volume | +--------------------------+---------------+--------------+----------+ | Air | 32-392 | .2375 | .1693 | | Oxygen | 44-405 | .2175 | .1553 | | Nitrogen | 32-392 | .2438 | .1729 | | Hydrogen | 54-388 | 3.4090 | 2.4141 | | Superheated Steam | | See table 25 | | | Carbon Monoxide | 41-208 | .2425 | .1728 | | Carbon Dioxide | 52-417 | .2169 | .1535 | | Methane | 64-406 | .5929 | .4505 | | Blast Fur. Gas (approx.) | ... | .2277 | ... | | Flue gas (approx.) | ... | .2400 | ... | +--------------------------+---------------+--------------+----------+
Latent heat is not lost, but reappears whenever the substances pa.s.s through a reverse cycle, from a gaseous to a liquid, or from a liquid to a solid state. It may, therefore, be defined as stated, as the heat which apparently disappears, or is lost to thermometric measurement, when the molecular const.i.tution of a body is being changed. Latent heat is expended in performing the work of overcoming the molecular cohesion of the particles of the substance and in overcoming the resistance of external pressure to change of volume of the heated body. Latent heat of evaporation, therefore, may be said to consist of internal and external heat, the former being utilized in overcoming the molecular resistance of the water in changing to steam, while the latter is expended in overcoming any resistance to the increase of its volume during formation. In evaporating a pound of water at 212 degrees to steam at 212 degrees, 897.6 B. t. u. are expended as internal latent heat and 72.8 B. t. u. as external latent heat. For a more detailed description of the changes brought about in water by sensible and latent heat, the reader is again referred to the chapter on "The Theory of Steam Making".
Ebullition--The temperature of ebullition of any liquid, or its boiling point, may be defined as the temperature which exists where the addition of heat to the liquid no longer increases its temperature, the heat added being absorbed or utilized in converting the liquid into vapor.
This temperature is dependent upon the pressure under which the liquid is evaporated, being higher as the pressure is greater.
TABLE 5
BOILING POINTS AT ATMOSPHERIC PRESSURE
+---------------------+--------------+ | | Degrees | | | Fahrenheit | +---------------------+--------------+ | Ammonia | 140 | | Bromine | 145 | | Alcohol | 173 | | Benzine | 212 | | Water | 212 | | Average Sea Water | 213.2 | | Saturated Brine | 226 | | Mercury | 680 | +---------------------+--------------+
Total Heat of Evaporation--The quant.i.ty of heat required to raise a unit of any liquid from the freezing point to any given temperature, and to entirely evaporate it at that temperature, is the total heat of evaporation of the liquid for that temperature. It is the sum of the heat of the liquid and the latent heat of evaporation.
To recapitulate, the heat added to a body is divided as follows:
Total heat = Heat to change the temperature + heat to overcome the molecular cohesion + heat to overcome the external pressure resisting an increase of volume of the body.
Where water is converted into steam, this total heat is divided as follows:
Total heat = Heat to change the temperature of the water + heat to separate the molecules of the water + heat to overcome resistance to increase in volume of the steam, = Heat of the liquid + internal latent heat + external latent heat, = Heat of the liquid + total latent heat of steam, = Total heat of evaporation.
The steam tables given on pages 122 to 127 give the heat of the liquid and the total latent heat through a wide range of temperatures.
Gases--When heat is added to gases there is no internal work done; hence the total heat is that required to change the temperature plus that required to do the external work. If the gas is not allowed to expand but is preserved at constant volume, the entire heat added is that required to change the temperature only.
Linear Expansion of Substances by Heat--To find the increase in the length of a bar of any material due to an increase of temperature, multiply the number of degrees of increase in temperature by the coefficient of expansion for one degree and by the length of the bar.
Where the coefficient of expansion is given for 100 degrees, as in Table 6, the result should be divided by 100. The expansion of metals per one degree rise of temperature increases slightly as high temperatures are reached, but for all practical purposes it may be a.s.sumed to be constant for a given metal.
TABLE 6
LINEAL EXPANSION OF SOLIDS AT ORDINARY TEMPERATURES
(Tabular values represent increase per foot per 100 degrees increase in temperature, Fahrenheit or centigrade)
+-------------------+--------------+----------------+----------------+ | | Temperature | | | | | Conditions[4]|Coefficient per |Coefficient per | | Substance | Degrees | 100 Degrees | 100 Degrees | | | Fahrenheit | Fahrenheit | Centigrade | +-------------------+--------------+----------------+----------------+ |Bra.s.s (cast) | 32 to 212 | .001042 | .001875 | |Bra.s.s (wire) | 32 to 212 | .001072 | .001930 | |Copper | 32 to 212 | .000926 | .001666 | |Gla.s.s (English | | | | |flint) | 32 to 212 | .000451 | .000812 | |Gla.s.s (French | | | | |flint) | 32 to 212 | .000484 | .000872 | |Gold | 32 to 212 | .000816 | .001470 | |Granite (average) | 32 to 212 | .000482 | .000868 | |Iron (cast) | 104 | .000589 | .001061 | |Iron (soft forged) | 0 to 212 | .000634 | .001141 | |Iron (wire) | 32 to 212 | .000800 | .001440 | |Lead | 32 to 212 | .001505 | .002709 | |Mercury | 32 to 212 | .009984[5] | .017971 | |Platinum | 104 | .000499 | .000899 | |Limestone | 32 to 212 | .000139 | .000251 | |Silver | 104 | .001067 | .001921 | |Steel (Bessemer | | | | |rolled, hard) | 0 to 212 | .00056 | .00101 | |Steel (Bessemer | | | | |rolled, soft) | 0 to 212 | .00063 | .00117 | |Steel (cast, | | | | |French) | 104 | .000734 | .001322 | |Steel (cast | | | | |annealed, English) | 104 | .000608 | .001095 | +-------------------+--------------+----------------+----------------+
High Temperature Measurements--The temperatures to be dealt with in steam-boiler practice range from those of ordinary air and steam to the temperatures of burning fuel. The gases of combustion, originally at the temperature of the furnace, cool as they pa.s.s through each successive bank of tubes in the boiler, to nearly the temperature of the steam, resulting in a wide range of temperatures through which definite measurements are sometimes required.
Of the different methods devised for ascertaining these temperatures, some of the most important are as follows:
1st. Mercurial pyrometers for temperatures up to 1000 degrees Fahrenheit.
2nd. Expansion pyrometers for temperatures up to 1500 degrees Fahrenheit.
3rd. Calorimetry for temperatures up to 2000 degrees Fahrenheit.
4th. Thermo-electric pyrometers for temperatures up to 2900 degrees Fahrenheit.
5th. Melting points of metal which flow at various temperatures up to the melting point of platinum 3227 degrees Fahrenheit.
6th. Radiation pyrometers for temperatures up to 3600 degrees Fahrenheit.
7th. Optical pyrometers capable of measuring temperatures up to 12,600 degrees Fahrenheit.[6] For ordinary boiler practice however, their range is 1600 to 3600 degrees Fahrenheit.
[Ill.u.s.tration: 228 Horse-power Babc.o.c.k & Wilc.o.x Boiler, Installed at the Wentworth Inst.i.tute, Boston, Ma.s.s.]
Table 7 gives the degree of accuracy of high temperature measurements.
TABLE 7
ACCURACY OF HIGH TEMPERATURE MEASUREMENTS[7]
+------------------------+------------------------+ | Centigrade | Fahrenheit | +-------------+----------+-------------+----------+ | | Accuracy | | Accuracy | | Temperature | Plus or | Temperature | Plus or | | Range | Minus | Range | Minus | | | Degrees | | Degrees | +-------------+----------+-------------+----------+ | 200- 500 | 0.5 | 392- 932 | 0.9 | | 500- 800 | 2 | 932-1472 | 3.6 | | 800-1100 | 3 | 1472-2012 | 5.4 | | 1100-1600 | 15 | 2012-2912 | 27 | | 1600-2000 | 25 | 2912-3632 | 45 | +-------------+----------+-------------+----------+
Mercurial Pyrometers--At atmospheric pressure mercury boils at 676 degrees Fahrenheit and even at lower temperatures the mercury in thermometers will be distilled and will collect in the upper part of the stem. Therefore, for temperatures much above 400 degrees Fahrenheit, some inert gas, such as nitrogen or carbon dioxide, must be forced under pressure into the upper part of the thermometer stem. The pressure at 600 degrees Fahrenheit is about 15 pounds, or slightly above that of the atmosphere, at 850 degrees about 70 pounds, and at 1000 degrees about 300 pounds.
Flue-gas temperatures are nearly always taken with mercurial thermometers as they are the most accurate and are easy to read and manipulate. Care must be taken that the bulb of the instrument projects into the path of the moving gases in order that the temperature may truly represent the flue gas temperature. No readings should be considered until the thermometer has been in place long enough to heat it up to the full temperature of the gases.
Expansion Pyrometers--Bra.s.s expands about 50 per cent more than iron and in both bra.s.s and iron the expansion is nearly proportional to the increase in temperature. This phenomenon is utilized in expansion pyrometers by enclosing a bra.s.s rod in an iron pipe, one end of the rod being rigidly attached to a cap at the end of the pipe, while the other is connected by a multiplying gear to a pointer moving around a graduated dial. The whole length of the expansion piece must be at a uniform temperature before a correct reading can be obtained. This fact, together with the lost motion which is likely to exist in the mechanism connected to the pointer, makes the expansion pyrometer unreliable; it should be used only when its limitations are thoroughly understood and it should be carefully calibrated. Unless the bra.s.s and iron are known to be of the same temperature, its action will be anomalous: for instance, if it be allowed to cool after being exposed to a high temperature, the needle will rise before it begins to fall. Similarly, a rise in temperature is first shown by the instrument as a fall. The explanation is that the iron, being on the outside, heats or cools more quickly than the bra.s.s.
Calorimetry--This method derives its name from the fact that the process is the same as the determination of the specific heat of a substance by the water calorimeter, except that in one case the temperature is known and the specific heat is required, while in the other the specific heat is known and the temperature is required. The temperature is found as follows:
A given weight of some substance such as iron, nickel or fire brick, is heated to the unknown temperature and then plunged into water and the rise in temperature noted.
If X = temperature to be measured, w = weight of heated body in pounds, W = weight of water in pounds, T = final temperature of water, t = difference between initial and final temperatures of water, s = known specific heat of body. Then X = T + Wt ws
Any temperatures secured by this method are affected by so many sources of error that the results are very approximate.
Thermo-electric Pyrometers--When wires of two different metals are joined at one end and heated, an electromotive force will be set up between the free ends of the wires. Its amount will depend upon the composition of the wires and the difference in temperature between the two. If a delicate galvanometer of high resistance be connected to the "thermal couple", as it is called, the deflection of the needle, after a careful calibration, will indicate the temperature very accurately.