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 [Pg 187] 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 assumes 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 assumed 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:
| C | = | N |
| (19) |
| 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 radiationis computed, | |
| T" | = | average temperature over period of combustion[39], | |
| T' | = | average temperature over period through which final radiationis 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 [Pg 188] combustion, and CD the time of final radiation. Therefore to apply Pfaundler’s correction, formula ([19]), to the data as represented by Fig. 25.