Part 37

The bomb is then placed in the calorimeter, which has been filled with a definite amount of water. This weight is the "water equivalent" of the apparatus, i. e., the weight of water, the temperature of which would be increased one degree for an equivalent increase in the temperature of the combined apparatus. It may be determined by calculation from the weights and specific heats of the various parts of the apparatus. Such a determination is liable to error, however, as the weight of the bomb lining can only be approximated, and a considerable portion of the apparatus is not submerged. Another method of making such a determination is by the adding of definite weights of warm water to definite amounts of cooler water in the calorimeter and taking an average of a number of experiments. The best method for the making of such a determination is probably the burning of a definite amount of resublimed naphthaline whose heat of combustion is known.

The temperature of the water in the water jacket of the calorimeter should be approximately that of the surrounding atmosphere. The temperature of the weighed amount of water in the calorimeter is made by some experimenters slightly greater than that of the surrounding air in order that the initial correction for radiation will be in the same direction as the final correction. Other experimenters start from a temperature the same or slightly lower than the temperature of the room, on the basis that the temperature after combustion will be slightly higher than the room temperature and the radiation correction be either a minimum or entirely eliminated.

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.

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 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:

| 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, T' = average temperature over period through which final radiation is computed.

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.