Calculate change in mass fraction, Chemistry

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Question

Table 1 shows the specific rate of breakage S_j and the values of the breakage distribution function b(i,j) of a mineral ore in a ball mill. Table 2 shows the size distribution of the feed.

Table 1 Specific rate of breakage S_j and the values of the breakage distribution function b(i,j) of a mineral ore in a ball mill based on 5 revolution of the mill.

Size Interval (µm) 150-106 106-75 75-53 53-37 37-0

Interval, j 1 2 3 4 5

Sj 0.65 0.55 0.40 0.35 0.00

b(1, j) 0.00 0.00 0.00 0.00 0.00

b(2, j) 0.35 0.00 0.00 0.00 0.00

b(3, j) 0.25 0.45 0.00 0.00 0.00

b(4, j) 0.20 0.30 0.60 0.00 0.00

b(5,j) 0.20 0.25 0.40 1.00 0.00

Table 2 Size distribution of the feed.

584_Calculate Change in Mass Fraction.png

(a) Which interval has the smallest absolute change in mass fraction after 1 min if the mill was operated at 5 rpm? Show your calculations.

(b) Given that the energy requirement for this ball milling process is 25 kJ·kg^-1. In 100 words or less, describe which model (or models) you would use to estimate the energy required to crush the same feed material to a different size distribution. Justify your answers.

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