Hey everyone,
I've been trying to figure out these two columns for this webassign. I used the equation given to us in class for an excel worksheet but still couldn't get it. Anyone have any ideas?

Consider a cooling cup of coffee whose initial temperature is 203°. The room temperature is held at 70°. Suppose k = 1/15

Time (minutes) Temp Euler's Method (dt = 5) Temp Euler's Method (dt = 1)
5
20
30
60

3/1/2007 7:37:55 PM

found from an old thread: just plug in your numbers

Quote :

"Quote : "initial temp = 210, room temp = 70, k = 1/16, what is the continuous solution equation? (use t as variable) thanks" Lets see I think the equation here is that the rate of temperatur change dT/dt is proportional to the difference from room temperature (T-70) according to the proportionality constant k=-1/16. That gives us the differential equation: dT/dt = k(T-70) Seperate variables, dT/(T-70) = kdt Integrate, ln|T-70| = kt + C1 Exponentiate, |T-70| = exp(kt+C1) = C2*exp(kt) This allows for two possible families of solutions, one where |T-70|<0 and another where |T-70|>0. Using +/- notation for this gives us T- 70 = (+/-)C2*exp(kt) Solving for T and introducing C3=(+/-)C2, T= 70 + C3*exp(kt) Now we know that T(t=0) = 210 = 70 +C3 thus C3= 140. Hence, T = 70 + 140*exp( (-1/16)*t ) Notice that as t goes to infinity we reach room temperature."

http://thewolfweb.com/message_topic.aspx?topic=391636

3/1/2007 8:36:10 PM

way to go hszaczek24, you actually helped someone instead of criticize them

3/1/2007 11:45:56 PM

Could someone help me with the first part of the quesiton where you have to find the differential equation? I have looked over the class notes and the post above and I just don't understand how to find the differential equation (I did find the continuous equation).

Also...how do you figure out the chart...I'm assuming that you just plug and chug numbers into one of the two equations found in the first part of the question but I'm not sure which numbers to plug!! Thanks a lot with the help.

3/2/2007 4:39:08 AM

My numbers are the same as aekantor fyi....thanks again

3/2/2007 4:39:37 AM

Thanks, BIG HELP!

3/2/2007 7:49:12 AM

you are welcome

3/3/2007 2:20:00 PM

Well I hope my solution works for you. However, they did say to use Euler's method. Now what my solution (quoted above) gives is the exact solution. You're not supposed to know that, rather you are supposed to do an iterative calculation (follow the algorithim of Euler's method).

That said, Webassign will probably take the exact answer just the same.

This is a general principle of WA, if confronted with an annoying numerical problem one should use a calculator to solve it exactly hence avoiding stupid arithmatic. Or you could just join one of the numerous organizations that have all the answers already.

3/5/2007 1:07:04 AM