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![[Post New]](/templates/default/images/icon_minipost_new.gif) 19 Mar 2008 12:55:21 IST
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Q A moth ball evaporates at a rate directly proportional to its surface area . At t = 0 its radius R = 15 cm . At t=2s its found that R =11cm. when will it disappear completely. plz ans with explanation Rates will be Given
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19 Mar 2008 13:00:30 IST
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it will disappear only at t=infinity...
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" Always remember money isn't everything but make sure you have made a lot of it before talking such nonsense!"
- Bill Gates |
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19 Mar 2008 13:04:09 IST
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sorry....calc mistake....15 to 11 in 2 sec... means...2cm takes 1 sec... so remaing...11 cm will tac 5.5 sec......so total 15 cm will melt in 5.5+2=7.5 sec.....it was only a calc mistake..as u can c it ive done the derivation!!!!!
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19 Mar 2008 13:05:00 IST
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no answer is 7.5 secs....i just posted the solution but i think the creator of the thread deleted it :(
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his is how: form the differential equation
-(dV/dt) = 4k*pi*r^2 where k is a constant of proportioanlity.....now write V's expression....the final differential equation in terms of r is
dr/dt = -k whose solution is
r(t) - r(0) = -kt
Put the values to get k = 2
finally, if T is the time for complete evaporation, we have
0 - 15 = -2T -----> T = 7.5 secs
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19 Mar 2008 13:09:10 IST
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welll...i have a doubt...
this might be analogous to a second order chemical reaction,
where radius acts as concentration...
so rate=K(r)*(r)
and these reaction go to completion only at t=infinty...
as the rate keeps decreasing as radius decreases...and hence T=infinty
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" Always remember money isn't everything but make sure you have made a lot of it before talking such nonsense!"
- Bill Gates |
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19 Mar 2008 13:12:14 IST
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this assumption does not have a logical basis :)
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21 Mar 2008 12:25:44 IST
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ans 7.5sec is right ty guys
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