Express this dustfall in milligrams per square meter per hour.?

Question

A typical rate of deposit of dust (dustfall) from unpolluted air was reported as 10 tons per square mile per month.

a) Express this dustfall in milligrams per square meter per hour.

b) If the dust has an average density of 2 g/cm^3, how long would it take to accumulate a layer of dust 1 mm thick?

Answer 1

problems,... what's a month?... what type of ton?

let's chose a 30 day month, & a 2000 pound ton, therefor :

20,000 pounds / 30 days =  666.67 pounds / day

666.67 pounds / 24 hours = 27.778 pounds / hour  

27.778 pounds / hour  @ 453,600 mg / pound = 1.26e7 mg

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that's 1.26e7 mg/hr per square mile

1.26e7 mg/hr-mi2 @ 1 mi2 /  2.590 e6 square meter m =

your answer: 4.865 mg/hr-m2

but giving them the benefit of the doubt, at best this is a 2 sigfig problem, you ought to round your answer at least off to 4.9 mg/hr-m2

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b) If the dust has an average density of 2 g/cm^3, how long would it take to accumulate a layer of dust 1 mm, (aka 0.1 cm) thick?

,

(2000 mg/cm3) ( 0.1 cm thick) = 200 mg / cm2

200mg/ cm2 @ 10,000 cm2 / m2 = 2e6 mg /m2

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(2e6 mg /m2) / (4.865 mg/hr-m2) = 4.111e5 hours

your answer is (1 sigfig) : 4e5 hours