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A plot of height of fall in air versus time of fall in air for 0.7 g droplet is shown in Fig.55.

4.2.2 Oxidation of Pure Iron Droplets

The oxidation of the iron droplets is recorded in Tables 34- to 39. Each table records the height and time of fall in air for the iron droplets. Against each droplet, its mass, temperature at fall and its oxygen analysis, are recorded. From the mass of the droplet the radius was determined and the oxygen value for a 0.7 g equivalent droplet was determined and recorded. The number of droplets varied for each height of fall and the data for each group of droplets was analysed statistically. For each group of droplets the sample mean was determined and the sample standard deviation calculated. The standard deviation or standard error of the mean was calculated by dividing the sample standard

deviation by the square root of the sample size. The 95 per cent confidence interval for the mean value was determined by reference to the t-distribution. The mean value was plotted on the graph by a circle and the limits of the 95 per cent confidence interval were recorded by a bar. It can be seen that using this technique the spread of the confidence interval tends to be inversely related

to the number of samples taken. Graphs were drawn for oxygen pick-up in mass$ versus height of fall in air, Fig. 56, and for oxygen pick-up versus time of fall in air, Fig. 57. It can be seen that the confidence limits for the 59 cm and 100 cm fall in air are much closer to the mean than those for the 37 cm and 90 cm fall in air values. The number of samples for the former were twenty and twenty-four respectively, whilst for the latter

six and four respectively. The results from eighty-three droplets were used to compute the two graphs. A line of best fit was

drawn through the oxygen pick-up versus height of fall in air points, originating at the zero of the graph. In the case of the

oxygen pick-up versus time of fall in air graph the best fit through the points was a straight line. Extrapolating the line back to the zero time axis the line did not pass through the origin but intercepted the mass per cent oxygen axis at about 0.005 mass$ oxygen.

The rate of oxidation of iron at 1600°C over the measured interval suggests that the reaction is zero order. The rate constant, k, is then simply given by mass$ oxygen per unit time. Taken from the graph this gives 0.215 mass$ oxygen per second. If the rate is related to the mass of oxygen picked up per unit area per unit time this value becomes 7 .6 mg oxygen per cm^ of iron surface per second.

4.2.3 Oxidation of Iron-Manganese Alloy Droplets

Three iron-manganese alloys were investigated, Fe-0.5$ Mn, Fe-0.7$ Mn and Fe-1.0$ Mn. The 0.5$ Mn alloy was investigated over five different heights in air and the results are recorded

in Tables 4-0 to 44-* These results are plotted in Figs.53 and 59. It can be seen that when oxygen pick-up is plotted against height of fall in air the form of the graph is similar to that for pure iron. In fact the values for the 75 cm, 100 cm and 118 cm fall in air are almost identical to the values recorded for the iron droplets. The difference is with the 37 cm and 50 cm values which are larger for the manganese alloy. When the results are plotted against time, the best fit is again a straight line through the points, again suggesting a zero order reaction over the time interval investigated. The rate constant for the alloy, k, is 0.173 mass$ oxygen per second or 6.10 mg oxygen per cm^ of iron alloy surface per second.

It is evident that the initial rate, compared to that of iron, is higher. The first point on the graph is at 37 cm or 0.15

second. If a line is drawn from the origin to this first point at

0.15s, this would give the minimum value of the initial rate constant. In this case it is 0.30 mass* oxygen per second or

10.6 mg oxygen per cm^ surface per second.

The second iron-manganese alloy, 0.7 mass$ Mn, was investi­ gated over six different fall heights in air. The results are recorded in Tables 45 to 50 and Figs.60 and 61. Compared to the Fe-0.5$ Mn alloy, the oxygen pick-up at each height interval for the Fe-0.7$ Mn alloy is marginally greater, except for the 113 cm fall. As in the previous cases, the best fit for the rate of oxidation is a straight line. The rate constant over the measured distance is 0.15s mass* oxygen per second or 5.50 mg oxygen per cm^ iron alloy surface per second. Again the minimum initial rate constant from zero time

to 0.15 s was calcualted by measuring the slope of the line