evaporation rate

**acosta0809** · February 16th 2010, 05:29 PM

this question is giving me a really hard time...

A spherical drop of radius r(t), r cms, t minutes evaporates at a rate proportional to its surface area. Given that the volume v(t)=4/3╥r^(3) and the surface area s(t)=4╥r^(2), write down an ODE for r(t).

I am very stuck i have no idea of where to begin, can anyone please help me, Thank you

**pickslides** · February 16th 2010, 06:11 PM

Originally Posted by acosta0809

r cms, t minutes evaporates at a rate proportional to its surface area. Given that the volume v(t)=4/3╥r^(3) and the surface area s(t)=4╥r^(2), write down an ODE for r(t).

I'll take a punt,

$\frac{dr}{dt} \propto 4\pi r^2 \implies \frac{dr}{dt} =k\times 4\pi r^2$

Now separating

$\frac{dr}{r^2} =k\times 4\pi~dt$

Can you solve this?

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