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#1 2006-01-16 01:57:29

jacs
Member
Registered: 2006-01-16
Posts: 2

Concentration of brine in cooling

Hi, my first post, and i need help with some applications of calculus to physics


A tank contains 100 litres of brine whose concentration is 3 grams/litres. Three litres of brine whose concentration is 2 grams/litre flow into the tank each minute and at the same time 3 litres of mixture flow out each minute.

Show that the quantity of salt, Q gram, in the tank at any time t is given by:
Q = 200 + 100e[sup]-0.03t[/sup]

i have managed to get Q = 200 - 100e[sup]-0.03t[/sup]


and cannot figure out why the minus is there, i have included the pdf of the working i have done so far, any help appreciated

thanks
jacs

View Image: brine.gif

Last edited by jacs (2006-01-16 02:05:35)

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#2 2006-01-16 04:11:27

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Concentration of brine in cooling

You use a different method for solving differential equations than I'm used to, and quite an awkward one at that.  See if you can follow this, and if you want, I can try to find the error in your steps.

Integrate both sides


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2006-01-16 09:51:00

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: Concentration of brine in cooling

Nice work, Ricky!

jacs wrote:

Show that the quantity of salt, Q gram, in the tank at any time t is given by:
Q = 200 + 100e[sup]-0.03t[/sup]

And, of course, the 100e[sup]-0.03t[/sup] term decreases with t, so it should be added.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#4 2006-01-16 11:42:37

jacs
Member
Registered: 2006-01-16
Posts: 2

Re: Concentration of brine in cooling

thank you thankyou thankyou  I see it now.... i had the negative log and so cheated assuming that the 3Q was 300 instead of 900 (which i secretly knew was wrong...lol....but coudnt get rid of negative log so sort fudged the results)

what i needed was just the clever maniplutaion of the minus...ohhh soo easy now i see

thanks

jacs

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