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A wet porous substance in the open air losses its moisture at a rate proportional to the moisture content. If a sheet hung in the wind loses half of its moisture during the first hour, when will it have lost 95% moisture, weather conditions remaining the same.

A wet porous substance in the open air losses its moisture at a rate proportional to the moisture content. If a sheet hung in the wind loses half of its moisture during the first hour, when will it have lost 95% moisture, weather conditions remaining the same.

Grade:Upto college level

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Let ‘C’ be the moisture content at any time ‘t’
Given:
\frac{dC}{dt} = aC, a = constant
C* = Initial moisture
\int_{C*}^{C*/2}\frac{dC}{C} = \int_{0}^1{}adt
(lnC)_{C*}^{C*/2} = (at)_{0}^{1}
\Rightarrow a = -ln2
\int_{C*}^{.05C*}\frac{dC}{C} = \int_{0}^{t}-ln2.dt
\Rightarrow t = \frac{ln20}{ln2} hr
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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