While no experiments have been made to show conclusively which of these methods is the better, the latter is generally used.
After the bomb has been placed in the calorimeter, it is filled with oxygen from a tank until the pressure reaches from 20 to 25 atmospheres.
The lower pressure will be sufficient in all but exceptional cases.
Connection is then made to a current from the dry batteries in series so arranged as to allow completion of the circuit with a switch. The current from a lighting system should not be used for ignition, as there is danger from sparking in burning the fuse, which may effect the results. The apparatus is then ready for the test.
Unquestionably the best method of taking data is by the use of co-ordinate paper and a plotting of the data with temperatures and time intervals as ordinates and abscissae. Such a graphic representation is shown in Fig. 25.
[Graph: Temperature-- C. against Time--Hours and Minutes
Fig. 25. Graphic Method of Recording Bomb Calorimeter Results]
After the bomb is placed in the calorimeter, and before the coal is ignited, readings of the temperature of the water should be taken at one minute intervals for a period long enough to insure a constant rate of change, and in this way determine the initial radiation. The coal is then ignited by completing the circuit, the temperature at the instant the circuit is closed being considered the temperature at the beginning of the combustion. After ignition the readings should be taken at one-half minute intervals, though because of the rapidity of the mercury"s rise approximate readings only may be possible for at least a minute after the firing, such readings, however, being sufficiently accurate for this period. The one-half minute readings should be taken after ignition for five minutes, and for, say, five minutes longer at minute intervals to determine accurately the final rate of radiation.
Fig. 25 shows the results of such readings, plotted in accordance with the method suggested. It now remains to compute the results from this plotted data.
The radiation correction is first applied. Probably the most accurate manner of making such correction is by the use of Pfaundler"s method, which is a modification of that of Regnault. This a.s.sumes that in starting with an initial rate of radiation, as represented by the inclination of the line AB, Fig. 25, and ending with a final radiation represented by the inclination of the line CD, Fig. 25, that the rate of radiation for the intermediate temperatures between the points B and C are proportional to the initial and final rates. That is, the rate of radiation at a point midway between B and C will be the mean between the initial and final rates; the rate of radiation at a point three-quarters of the distance between B and C would be the rate at B plus three-quarters of the difference in rates at B and C, etc. This method differs from Regnault"s in that the radiation was a.s.sumed by Regnault to be in each case proportional to the difference in temperatures between the water of the calorimeter and the surrounding air plus a constant found for each experiment. Pfaundler"s method is more simple than that of Regnault, and the results by the two methods are in practical agreement.
Expressed as a formula, Pfaundler"s method is, though not in form given by him:
_ _ | R" - R | C = N|R + ------ (T" - T)| (19) |_ T" - T _|
Where C = correction in degree centigrade, N = number of intervals over which correction is made, R = initial radiation in degrees per interval, R" = final radiation in degrees per interval, T = average temperature for period through which initial radiation is computed, T" = average temperature over period of combustion[39], T" = average temperature over period through which final radiation is computed.[39]
The application of this formula to Fig. 25 is as follows:
As already stated, the temperature at the beginning of combustion is the reading just before the current is turned on, or B in Fig. 25. The point C or the temperature at which combustion is presumably completed, should be taken at a point which falls well within the established final rate of radiation, and not at the maximum temperature that the thermometer indicates in the test, unless it lies on the straight line determining the final radiation. This is due to the fact that in certain instances local conditions will cause the thermometer to read higher than it should during the time that the bomb is transmitting heat to the water rapidly, and at other times the maximum temperature might be lower than that which would be indicated were readings to be taken at intervals of less than one-half minute, _i. e._, the point of maximum temperature will fall below the line determined by the final rate of radiation. With this understanding AB, Fig. 25, represents the time of initial radiation, BC the time of combustion, and CD the time of final radiation. Therefore to apply Pfaundler"s correction, formula (19), to the data as represented by Fig. 25.
N = 6, R = 0, R" = .01, T = 20.29, T" = 22.83,
20.29 + 22.54 + 22.84 + 22.88 + 22.87 + 22.86 T" = --------------------------------------------- = 22.36 6
_ _ | .01 - 0 | C = 6|0 + -------------(22.36 - 20.29)| |_ 22.85 - 20.29 _|
= 6 .008 = .048
Pfaundler"s formula while simple is rather long. Mr. E. H. Peabody has devised a simpler formula with which, under proper conditions, the variation from correction as found by Pfaundler"s method is negligible.
It was noted throughout an extended series of calorimeter tests that the maximum temperature was reached by the thermometer slightly over one minute after the time of firing. If this period between the time of firing and the maximum temperature reported was exactly one minute, the radiation through this period would equal the radiation per one-half minute _before firing_ plus the radiation per one-half minute _after the maximum temperature is reached_; or, the radiation through the one minute interval would be the average of the radiation per minute before firing and the radiation per minute after the maximum. A plotted chart of temperatures would take the form of a curve of three straight lines (B, C", D) in Fig. 25. Under such conditions, using the notation as in formula (19) the correction would become,
2R + 2R"
C = ------- + (N - 2)R", or R + (N - 1)R" (20) 2
This formula may be generalized for conditions where the maximum temperature is reached after a period of more than one minute as follows:
Let M = the number of intervals between the time of firing and the maximum temperature. Then the radiation through this period will be an average of the radiation for M intervals before firing and for M intervals after the maximum is recorded, or
MR + MR" M M C = ------- + (N - M)R" = - R + (N - -)R" (21) 2 2 2
In the case of Mr. Peabody"s deductions M was found to be approximately 2 and formula (21) becomes directly, C = R + (N - 1)R" or formula (20).
The corrections to be made, as secured by the use of this formula, are very close to those secured by Pfaundler"s method, where the point of maximum temperature is not more than five intervals later than the point of firing. Where a longer period than this is indicated in the chart of plotted temperatures, the approximate formula should not be used. As the period between firing and the maximum temperature is increased, the plotted results are further and further away from the theoretical straight line curve. Where this period is not over five intervals, or two and a half minutes, an approximation of the straight line curve may be plotted by eye, and ordinarily the radiation correction to be applied may be determined very closely from such an approximated curve.
Peabody"s approximate formula has been found from a number of tests to give results within .003 degrees Fahrenheit for the limits within which its application holds good as described. The value of M, which is not necessarily a whole number, should be determined for each test, though in all probability such a value is a constant for any individual calorimeter which is properly operated.
The correction for radiation as found on page 188 is in all instances to be added to the range of temperature between the firing point and the point chosen from which the final radiation is calculated. This corrected range multiplied by the water equivalent of the calorimeter gives the heat of combustion in calories of the coal burned in the calorimeter together with that evolved by the burning of the fuse wire.
The heat evolved by the burning of the fuse wire is found from the determination of the actual weight of wire burned and the heat of combustion of one milligram of the wire (1.7 calories), _i. e._, multiply the weight of wire used by 1.7, the result being in gram calories or the heat required to raise one gram of water one degree centigrade.
Other small corrections to be made are those for the formation of nitric acid and for the combustion of sulphur to sulphuric acid instead of sulphur dioxide, due to the more complete combustion in the presence of oxygen than would be possible in the atmosphere.
To make these corrections the bomb of the calorimeter is carefully washed out with water after each test and the amount of acid determined from t.i.trating this water with a standard solution of ammonia or of caustic soda, all of the acid being a.s.sumed to be nitric acid. Each cubic centimeter of the ammonia t.i.trating solution used is equivalent to a correction of 2.65 calories.
As part of acidity is due to the formation of sulphuric acid, a further correction is necessary. In burning sulphuric acid the heat evolved per gram of sulphur is 2230 calories in excess of the heat which would be evolved if the sulphur burned to sulphur dioxide, or 22.3 calories for each per cent of sulphur in the coal. One cubic centimeter of the ammonia solution is equivalent to 0.00286 grams of sulphur as sulphuric acid, or to 0.286 22.3 = 6.38 calories. It is evident therefore that after multiplying the number of cubic centimeters used in t.i.trating by the heat factor for nitric acid (2.65) a further correction of 6.38 - 2.65 = 3.73 is necessary for each cubic centimeter used in t.i.trating sulphuric instead of nitric acid. This correction will be 3.73/0.297 = 13 units for each 0.01 gram of sulphur in the coal.
The total correction therefore for the aqueous nitric and sulphuric acid is found by multiplying the ammonia by 2.65 and adding 13 calories for each 0.01 gram of sulphur in the coal. This total correction is to be deducted from the heat value as found from the corrected range and the amount equivalent to the calorimeter.
After each test the pan in which the coal has been burned must be carefully examined to make sure that all of the sample has undergone complete combustion. The presence of black specks ordinarily indicates unburned coal, and often will be found where the coal contains bone or slate. Where such specks are found the tests should be repeated. In testing any fuel where it is found difficult to completely consume a sample, a weighed amount of naphthaline may be added, the total weight of fuel and naphthaline being approximately one gram. The naphthaline has a known heat of combustion, samples for this purpose being obtainable from the United States Bureau of Standards, and from the combined heat of combustion of the fuel and naphthaline that of the former may be readily computed.
The heat evolved in burning of a definite weight of standard naphthaline may also be used as a means of calibrating the calorimeter as a whole.
COMBUSTION OF COAL
The composition of coal varies over such a wide range, and the methods of firing have to be altered so greatly to suit the various coals and the innumerable types of furnaces in which they are burned, that any instructions given for the handling of different fuels must of necessity be of the most general character. For each kind of coal there is some method of firing which will give the best results for each individual set of conditions. General rules can be suggested, but the best results can be obtained only by following such methods as experience and practice show to be the best suited to the specific conditions.
The question of draft is an all important factor. If this be insufficient, proper combustion is impossible, as the suction in the furnace will not be great enough to draw the necessary amount of air through the fuel bed, and the gases may pa.s.s off only partially consumed. On the other hand, an excessive draft may cause losses due to the excess quant.i.ties of air drawn through holes in the fire. Where coal is burned however, there are rarely complaints from excessive draft, as this can be and should be regulated by the boiler damper to give only the draft necessary for the particular rate of combustion desired. The draft required for various kinds of fuel is treated in detail in the chapter on "Chimneys and Draft". In this chapter it will be a.s.sumed that the draft is at all times ample and that it is regulated to give the best results for each kind of coal.
TABLE 40
ANTHRACITE COAL SIZES
_________________________________________________________________ | | | | | | | Testing Segments | | | Round Mesh | Standard Square | | | | Mesh | | Trade Name |__________________|__________________| | | | | | | | | Through | Over | Through | Over | | | Inches | Inches | Inches | Inches | |___________________________|_________|________|_________|________| | | | | | | | Broken | 4-1/2 | 3-1/4 | 4 | 2-3/4 | | Egg | 3-1/4 | 2-3/8 | 2-3/4 | 2 | | Stove | 2-3/8 | 1-5/8 | 2 | 1-3/8 | | Chestnut | 1-5/8 | 7/8 | 1-3/8 | 3/4 | | Pea | 7/8 | 5/8 | 3/4 | 1/2 | | No. 1 Buckwheat | 5/8 | 3/8 | 1/2 | 1/4 | | No. 2 Buckwheat or Rice | 3/8 | 3/16 | 1/4 | 1/8 | | No. 3 Buckwheat or Barley | 3/16 | 3/32 | 1/8 | 1/16 | |___________________________|_________|________|_________|________|
Anthracite--Anthracite coal is ordinarily marketed under the names and sizes given in Table 40.
The larger sizes of anthracite are rarely used for commercial steam generating purposes as the demand for domestic use now limits the supply. In commercial plants the sizes generally found are Nos. 1, 2 and 3 buckwheat. In some plants where the finer sizes are used, a small percentage of bituminous coal, say, 10 per cent, is sometimes mixed with the anthracite and beneficial results secured both in economy and capacity.
Anthracite coal should be fired evenly, in small quant.i.ties and at frequent intervals. If this method is not followed, dead spots will appear in the fire, and if the fire gets too irregular through burning in patches, nothing can be done to remedy it until the fire is cleaned as a whole. After this grade of fuel has been fired it should be left alone, and the fire tools used as little as possible. Owing to the difficulty of igniting this fuel, care must be taken in cleaning fires.
The intervals of cleaning will, of course, depend upon the nature of the coal and the rate of combustion. With the small sizes and moderately high combustion rates, fires will have to be cleaned twice on each eight-hour shift. As the fires become dirty the thickness of the fuel bed will increase, until this depth may be 12 or 14 inches just before a cleaning period. In cleaning, the following practice is usually followed: The good coal on the forward half of the grate is pushed to the rear half, and the refuse on the front portion either pulled out or dumped. The good coal is then pulled forward onto the front part of the grate and the refuse on the rear section dumped. The remaining good coal is then spread evenly over the whole grate surface and the fire built up with fresh coal.
A ratio of grate surface to heating surface of 1 to from 35 to 40 will under ordinary conditions develop the rated capacity of a boiler when burning anthracite buckwheat. Where the finer sizes are used, or where overloads are desirable, however, this ratio should preferably be 1 to 25 and a forced blast should be used. Grates 10 feet deep with a slope of 1 inches to the foot can be handled comfortably with this cla.s.s of fuel, and grates 12 feet deep with the same slope can be successfully handled. Where grates over 8 feet in depth are necessary, shaking grates or overlapping dumping grates should be used. Dumping grates may be applied either for the whole grate surface or to the rear section. Air openings in the grate bars should be made from 3/16 inch in width for No. 3 buckwheat to 5/16 inch for No. 1 buckwheat. It is important that these air openings be uniformly distributed over the whole surface to avoid blowing holes in the fire, and it is for this reason that overlapping grates are recommended.
No air should be admitted over the fire. Steam is sometimes introduced into the ashpit to soften any clinker that may form, but the quant.i.ty of steam should be limited to that required for this purpose. The steam that may be used in a steam jet blower for securing blast will in certain instances a.s.sist in softening the clinker, but a much greater quant.i.ty may be used by such an apparatus than is required for this purpose. Combustion arches sprung above the grates have proved of advantage in maintaining a high furnace temperature and in a.s.sisting in the ignition of fresh coal.
Stacks used with forced blast should be of such size as to insure a slight suction in the furnace under any conditions of operation. A blast up to 3 inches of water should be available for the finer sizes supplied by engine driven fans, automatically controlled by the boiler pressure.