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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

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

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

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"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..."

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Concentration of brine in cooling

Nice work, Ricky!

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.

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

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