## K MtMr

where k* = passage probability of the material with a given size at time t, or passage rate factor, (s~n) and n = 1 — m where m is a constant.

Upon solving this equation for M and substituting 1— n for m, the resulting model is:

where Mt = total mass of the material remaining on the sieve at time t (grams), Mr = material mass which does not pass the sieve (i.e. the sieve residue after infinite sieving time) (gram) and k = passage probability of the material with a given size at time t, or passage rate factor (s_1).

This model assumes that, after a time, k becomes independent of time and particle size. This occurs when the smallest particles have passed through the sieve and those left on the sieve are of a size close to the sieve opening. However, the sieving constant (k) is not guaranteed to be constant. For example, it may change with the depth of material on the sieve and hence change as M changes. Thus, one difficulty in using the above equation lies in describing how k changes with experimental conditions or time.

Integrating the above equation (setting Mr = 0) with the application of initial conditions yields:

where M = cumulative mass of material passed at sieving time t (grams) and M0 = cumulative mass of the material that would pass at infinite sieving time (grams). Note that M + Mt = M0. The rate constant can be determined empirically or deduced from physical principles. In the latter case k is defined as:

## Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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