Question

A small metal bar whose initial temperature was 20 C is dropped intoa large container of boiling water. How long will it take the bar to reach 90 C if it is known that it's temperature increases 2 C in 1 secnd. Howlong will it ake the bar to reach 98 C

Answer 1

\[T_m=100\]
\[\frac{dT}{dt}=k(T-100)\]

Answer 2

\[2=k(90-100)\]

2=-10k

-.2=k

\[\frac{dT}{dt}=k(T-100)\]

ln(T-100)=-.2t+c

\[T=100+ce^{-.2t}\]

Answer 3

\[20=100+ce^{-.2t}\]

-80=c

Answer 4

\[98=100-80e^{-.2t}\]

\[\frac{-2}{-80}=e^{-.2t}\]

\[ln(.025)=-.2t\]

\[\frac{ln(.025)}{-.2}=t\]

Answer 5

did icorrectly use the information to find k, since
\[\frac{dT}{dt}=2\]

Answer 6

the answer is like 86 seconds and i got like 16

Answer 7

hmm your answer makes sense, does it give you any formulas you have to work with?

Answer 8

only newtons law of cooling

Answer 9

ok one sec

Answer 10

i'm just confused allout by this because if it increases two degrees per seconds from 20 degrees it's a difference of 70 degrees

Answer 11

common sense woul say that it would take half that to get it to 90 degrees

Answer 12

which would be 35 seconds which is still no where near 82 seconds

Answer 13

unless for some reason the temperature has tobe in farenheit

Answer 14

hmm not too sure about this one either, but I did manage to find this

http://faculty.frostburg.edu/math/rcforsythe/Math%20432/Solutions/Exam%202,%20Spring%202011%20--%20Solutions.pdf

It's #2 in the pdf

Answer 15

yeah that one is like most in the book... this one has the rate in it though =/

Answer 16

it seems i have the rigt equation just the answer is wrong?

Answer 17

I think it's the same problem, just worded differently

Answer 18

ahh it is.. wow thanks lol

Answer 19

that's a weird way to word a problem though. makes sense

Answer 20

that's great it does