Question #105478
A wet porus substance in the open air loses its moisture at a rate proportional to the
moisture content, if a sheet hung in the wind loses half its moisture during the first
hour, then find the time when it has lost 95% moisture provided the weather
conditions remain the same.
1
Expert's answer
2020-03-17T13:56:59-0400

Let the moisture content be m.Thus, rate of moisture loss is given by dm/dt-dm/dt .

Given; dm/dtm    dm/dt=λm-{dm/dt} \propto m \implies dm/dt = -\lambda m , where λ\lambda is a constant.

dm/m=λdt\int dm/m =-\lambda \int dt

    m=m0eλt\implies m=m_0e^{- \lambda t} ; where m0m_0 is the initial moisture content at t=0t=0 .

Also given, m0/2=m0eλ    λ=(ln2)hr1m_0/2=m_0e^{-\lambda} \implies \lambda =(ln2 )hr^{-1}

If 95% moisture is lost at time t; then m=5%(m0)=0.05m0m=5\%(m_0)=0.05m_0

Thus, 0.05m0=m0etln2    t=log2(20)=4.322hr.=259.3min.0.05 m_0=m_0e^{-t*ln2} \implies t=log_2(20)=4.322hr.=259.3min.

Hence, the time when it has lost 95% moisture provided the weather conditions remain the same is after 4.322 hours.


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