Wet porous substances in the open air loses its moisture at a rate proportional to its moisture content. If…

Wet porous substances in the open air loses its moisture at a rate proportional to its moisture content. If a sheet hung in the wind loses half its moisture during the first hour, then the time when it would have lost 99.9% of its moisture is (weather condition remaining same)
  1. more than 100 h
  2. more than 10 h
  3. approximately 10 h
  4. approximately 9 h

Solution

Let M be the moisture content in the porous substance at any time t and M0 be the initial moisture content.

Then, dMdt=−kM ⇒M=Ce−kt

When t=0; M=M0

⇒C=M0

⇒M=M0e−kt

When, t=1, M=M02

⇒k=ln2

M=M0e−tln2

When M=M01000,

then t=ln21000=9.98≃10 h

Asked in: MHT CET Full Test 10

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