Question 1129390: Can someone please help explain how to solve the problem:
A pot of boiling soup with an internal temperature of 100° Fahrenheit was taken off the stove to cool in a 69°F room. After fifteen minutes, the internal temperature of the soup was 93°F.
To the nearest minute, how long will it take the soup to cool to 81°F?
Found 3 solutions by addingup, solver91311, ikleyn:
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! 100-93 = 7 the temperature cooled by 7 degrees in 15 minutes. Assuming it continues to cool at a constant rate, it will contimue to cool at 7/15 degrees per minute = 0.467 degrees.
It has to cool another 93-81 = 12 degrees, and 12/0.467 = 25.7 minutes
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
Newton's Formula for Cooling:
\ =\ T_s\ +\ \(T_o\ -\ T_s\)e^{-kt})
where ) is the temperature of the object at time  ,  is the temperature of the surrounding environment,  is the initial temperature of the object, and  is a constant related to the nature of the object.
First, we need the value of for this particular flavor of soup.
e^{-15k})
Solve for , then substitute that value into
e^{-kt})
and then solve for which will be the elapsed time in minutes since cooling began. Subtract 15 if you want the time between when the soup was 93 degrees and when it cooled to 81 degrees.
The math works out with this one, but there is one huge problem with the way this question is posed as it relates to the real world. Soup (or any other water-based liquid for that matter) does not boil at 100 degrees Fahrenheit. It boils at 212 degrees Fahrenheit or 100 degrees Celsius. 93 degree F soup would be pee-warm, and 81 degree F soup would be cold. Remember, your body is 98.6 degrees F if you are reasonably healthy. So whoever wrote this question is suffering from a severe case of recto-cranial inversion.
John
My calculator said it, I believe it, that settles it
Answer by ikleyn(52792)  (Show Source):
You can put this solution on YOUR website! .
Be very careful with the "solution" by @addingup.
It has nothing in common with reality and with the way on how the problem should be solved.
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Comment from student : Thanks and yes, by skimming through his explanation I noticed that the solution given did not
align properly with the method needed to solve the equation. I’ll work on the problem a few more times and see what answer I arrive to.
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My response : See the lesson
- Solving problem on Newton Law of cooling
in this site.
Very similar problem (a TWIN) was solved there with slighly different input numbers.
It is your TEMPLATE.
Read attentively, and then solve your problem in the same way.
H a p p y l e a r n i n g ! !
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