Chapter 7
British Thermal Unit--The quantitative measure of heat is the British thermal unit, ordinarily written B. t. u. This is the quantity of heat required to raise the temperature of one pound of pure water one degree at 62 degrees Fahrenheit; that is, from 62 degrees to 63 degrees. In the metric system this unit is the _calorie_ and is the heat necessary to raise the temperature of one kilogram of pure water from 15 degrees to 16 degrees centigrade. These two definitions lead to a discrepancy of 0.03 of 1 per cent, which is insignificant for engineering purposes, and in the following the B. t. u. is taken with this discrepancy ignored. The discrepancy is due to the fact that there is a slight difference in the specific heat of water at 15 degrees centigrade and 62 degrees Fahrenheit. The two units may be compared thus:
1 Calorie = 3.968 B. t. u. 1 B. t. u. = 0.252 Calories.
_Unit_ _Water_ _Temperature Rise_ 1 B. t. u. 1 Pound 1 Degree Fahrenheit 1 Calorie 1 Kilogram 1 Degree centigrade
But 1 kilogram = 2.2046 pounds and 1 degree centigrade = 9/5 degree Fahrenheit.
Hence 1 calorie = (2.2046 × 9/5) = 3.968 B. t. u.
The heat values in B. t. u. are ordinarily given per pound, and the heat values in calories per kilogram, in which case the B. t. u. per pound are approximately equivalent to 9/5 the calories per kilogram.
As determined by Joule, heat energy has a certain definite relation to work, one British thermal unit being equivalent from his determinations to 772 foot pounds. Rowland, a later investigator, found that 778 foot pounds were a more exact equivalent. Still later investigations indicate that the correct value for a B. t. u. is 777.52 foot pounds or approximately 778. The relation of heat energy to work as determined is a demonstration of the first law of thermo-dynamics, namely, that heat and mechanical energy are mutually convertible in the ratio of 778 foot pounds for one British thermal unit. This law, algebraically expressed, is W = JH; W being the work done in foot pounds, H being the heat in B. t. u., and J being Joules equivalent. Thus 1000 B. t. u.'s would be capable of doing 1000 × 778 = 778000 foot pounds of work.
Specific Heat--The specific heat of a substance is the quantity of heat expressed in thermal units required to raise or lower the temperature of a unit weight of any substance at a given temperature one degree. This quantity will vary for different substances For example, it requires about 16 B. t. u. to raise the temperature of one pound of ice 32 degrees or 0.5 B. t. u. to raise it one degree, while it requires approximately 180 B. t. u. to raise the temperature of one pound of water 180 degrees or one B. t. u. for one degree.
If then, a pound of water be considered as a standard, the ratio of the amount of heat required to raise a similar unit of any other substance one degree, to the amount required to raise a pound of water one degree is known as the specific heat of that substance. Thus since one pound of water required one B. t. u. to raise its temperature one degree, and one pound of ice requires about 0.5 degrees to raise its temperature one degree, the ratio is 0.5 which is the specific heat of ice. To be exact, the specific heat of ice is 0.504, hence 32 degrees × 0.504 = 16.128 B. t. u. would be required to raise the temperature of one pound of ice from 0 to 32 degrees. For solids, at ordinary temperatures, the specific heat may be considered a constant for each individual substance, although it is variable for high temperatures. In the case of gases a distinction must be made between specific heat at constant volume, and at constant pressure.
Where specific heat is stated alone, specific heat at ordinary temperature is implied, and _mean_ specific heat refers to the average value of this quantity between the temperatures named.
The specific heat of a mixture of gases is obtained by multiplying the specific heat of each constituent 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 pass 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 | | Brass (yellow) | 32 | .0883 | | Glass (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 pass 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 constitution 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 quantity 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 assumed 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 | +-------------------+--------------+----------------+----------------+ |Brass (cast) | 32 to 212 | .001042 | .001875 | |Brass (wire) | 32 to 212 | .001072 | .001930 | |Copper | 32 to 212 | .000926 | .001666 | |Glass (English | | | | |flint) | 32 to 212 | .000451 | .000812 | |Glass (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 pass 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.
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--Brass expands about 50 per cent more than iron and in both brass and iron the expansion is nearly proportional to the increase in temperature. This phenomenon is utilized in expansion pyrometers by enclosing a brass 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 brass 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 brass.
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.
In the thermo-electric pyrometer of Le Chatelier, the wires used are platinum and a 10 per cent alloy of platinum and rhodium, enclosed in porcelain tubes to protect them from the oxidizing influence of the furnace gases. The couple with its protecting tubes is called an "element". The elements are made in different lengths to suit conditions.
It is not necessary for accuracy to expose the whole length of the element to the temperature to be measured, as the electromotive force depends only upon the temperature of the juncture at the closed end of the protecting tube and that of the cold end of the element. The galvanometer can be located at any convenient point, since the length of the wires leading to it simply alter the resistance of the circuit, for which allowance may be made.
The advantages of the thermo-electric pyrometer are accuracy over a wide range of temperatures, continuity of readings, and the ease with which observations can be taken. Its disadvantages are high first cost and, in some cases, extreme delicacy.