Newton's Cooling Law: metal removed from oven at 550 degrees

[gwen01]

I placed into math 107 at my community college and it is way over my head. I desperately need help with a take home test that is due tomorrow. Here's the problem:

A piece of metal is removed from an oven at 550 degrees. After 30 minutes it has cooled to 425 degrees. Room temperature is 60 degrees.

Q1. What is the temperature after one hour 15 minutes?
Q2. How long until it reaches 100 degrees?

I was sick the day we learned Newton's Law of Cooling and i cannot figure this out on my own, can someone please help me figure this out step by step? Thanks!

 

[galactus]

Re: Newton's Cooling Law HELP!

We can start with the formula: \(\displaystyle T=(T_{0}-C)e^{kt}+C\)

Where T=the temperature at sometime t, C=the temp of the surrounding medium(in this case, 60), T_0=the temperature at t=0.

We need to use the initial condition, 425 at 1/2 hr, to find k then plug in our value for t=5/4 hour to find the temperature at that time.

\(\displaystyle 425=(550-60)e^{\frac{k}{2}}+60\)

\(\displaystyle 365=490e^{\frac{k}{2}}\)

\(\displaystyle \frac{73}{98}=e^{\frac{k}{2}}\)

\(\displaystyle k=2ln(\frac{73}{98})\approx{-.58902}\)

Your formula is then \(\displaystyle T=490e^{2ln(\frac{73}{98})t}+60\)

Now, use this value of k and sub it into your formula along with t=5/4 and you will find your temperature after 1 hour and 15 minutes. I used 5/4 hours because that is equal to 1 hour and 15 minutes. For part b, you will have to set the equation equal to 100 and solve for t.

The above formula is derived using separation of variables and integration. Do you have to do that as well, from scratch?.
If you do, let me know. We can go through the derivation.

 

[stapel]

I placed into math 107 at my community college and it is way over my head.

This is exactly why people shouldn't try to "game" the placement test. You have somehow managed to fool the process into thinking that you're ready for material which is, you state, "way over [your] head". The usual result is just what you've encountered: frustration, and a perfectly-understandable inability to keep up. Mathematical topics are very often sequential; by jumping ahead, you may have missed a great deal of what is needed to succeed in your current course.

I desperately need help with a take home test that is due tomorrow.

Probably the best solution, rather than having us complete your take-home tests for you, is to have a serious heart-to-heart with your academic advisor. From experience, I know that the customary result of being placed into a math course "way over one's head" is repeated failure. It is usually quicker, easier, and better to back up to a course more approriate to your level of experience, and start over from back there. You'll end up passing this course sooner, and with a much better understanding of the content.

My best wishes to you!

Eliz.

 

[Deleted member 4993]

I placed into math 107 at my community college and it is way over my head. I desperately need help with a take home test that is due tomorrow. Here's the problem:

A piece of metal is removed from an oven at 550 degrees. After 30 minutes it has cooled to 425 degrees. Room temperature is 60 degrees.

Q1. What is the temperature after one hour 15 minutes?
Q2. How long until it reaches 100 degrees?

I was sick the day we learned Newton's Law of Cooling and i cannot figure this out on my own, can someone please help me figure this out step by step? Thanks!

Should you be asking for help in a test????