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Math Help - Newton's Cooling Law HELP!

  1. #1
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    Newton's Cooling Law HELP!

    I'm new to math! 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.

    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!
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  2. #2
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    Quote Originally Posted by gwen01 View Post
    I'm new to math! 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.

    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!
    You just need to memorize the Law of Cooling.

    The formula is T(t)=T_{s}+(T_{0}-T_{s})e^{-kt}

    Without doing the whole problem for you, T(t) is the temperature of what is being cooled at any time t, T_{s} is the temperature of the surrounding area, after you have removed it from being heated.

    Are you told T_{s}? You did not give it here, and it's pretty important to know.

    T_{0} is the temperature of the object at the moment you have removed it.

    Now that you know this, you can use the numbers you are given to solve for the constant k which is the cooling constant.

    For part a, simply plug in the new value your given using the k you just found, and solve for T(75)

    For part b, set T(t)=100 and solve for t
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    Quote Originally Posted by Kalter Tod View Post
    You just need to memorize the Law of Cooling.

    The formula is T(t)=T_{s}+(T_{0}-T_{s})e^{-kt}

    Without doing the whole problem for you, T(t) is the temperature of what is being cooled at any time t, T_{s} is the temperature of the surrounding area, after you have removed it from being heated.

    Are you told T_{s}? You did not give it here, and it's pretty important to know.

    T_{0} is the temperature of the object at the moment you have removed it.

    Now that you know this, you can use the numbers you are given to solve for the constant k which is the cooling constant.

    For part a, simply plug in the new value your given using the k you just found, and solve for T(75)

    For part b, set T(t)=100 and solve for t
    Thanks so much, that helps,

    BUT....
    does anyone not mind solving the whole thing? i'm still lost, and this is something i'm not going to have to do ever again, its just one test problem that i need solved so that i can forget about it forever and move on to the next chapter. i'm sorry for being so lame!
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  4. #4
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    Quote Originally Posted by gwen01 View Post
    Thanks so much, that helps,

    BUT....
    does anyone not mind solving the whole thing? i'm still lost, and this is something i'm not going to have to do ever again, its just one test problem that i need solved so that i can forget about it forever and move on to the next chapter. i'm sorry for being so lame!
    *Ahem*

    "Are you told ? You did not give it here, and it's pretty important to know."

    Without this value (which is, more or less, the temperature outside the oven) numerical answers can't be got .....
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  5. #5
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    Quote Originally Posted by mr fantastic View Post
    *Ahem*

    "Are you told ? You did not give it here, and it's pretty important to know."

    Without this value (which is, more or less, the temperature outside the oven) numerical answers can't be got .....
    ^^^^

    Aye. What he said. I'll be more than happy to work it out for you. Unfortunately, in it's current state, I can only solve for the values in terms of T_{s} which I doubt very seriously is the form your professor wants them in.
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  6. #6
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    Quote Originally Posted by Kalter Tod View Post
    You just need to memorize the Law of Cooling.

    The formula is T(t)=T_{s}+(T_{0}-T_{s})e^{-kt}

    Without doing the whole problem for you, T(t) is the temperature of what is being cooled at any time t, T_{s} is the temperature of the surrounding area, after you have removed it from being heated.

    Are you told T_{s}? You did not give it here, and it's pretty important to know.

    T_{0} is the temperature of the object at the moment you have removed it.


    Now that you know this, you can use the numbers you are given to solve for the constant k which is the cooling constant.

    For part a, simply plug in the new value your given using the k you just found, and solve for T(75)

    For part b, set T(t)=100 and solve for t
    Quote Originally Posted by mr fantastic View Post
    *Ahem*

    "Are you told ? You did not give it here, and it's pretty important to know."

    Without this value (which is, more or less, the temperature outside the oven) numerical answers can't be got .....
    WOOPS! Room temp is 60 degrees
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  7. #7
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    Quote Originally Posted by gwen01 View Post
    WOOPS! Room temp is 60 degrees
    Okay, then the problem is quite simple.

    The formula
    <br />
T(t)=T_{s}+(T_{0}-T_{s})e^{-kt}<br />

    <br />
425=60+(550-60)e^{-k30}<br />

    Rearranging, you get:

    <br />
365=490e^{-30k}<br />

    or
    \ln{.744}=-30k which if you solve for k, you should get k=.00986

    Now that you have solved for k, you can use it solve the first and second questions.

    Part a: T(75)=60+(550-60)e^{-75k} which when solved, gives you: T(75)=293.903

    For part b: T(t)=100=60+(550-60)e^{-kt}

    Solving for t, you should get t=254.11
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  8. #8
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    Thank you so much!!!! in the future i will attend class regularly to avoid this happening agian.

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