SOLUTION: A pan of water is brought to a boil and then removed from the heat. Every 5 minutes thereafter the difference between the termperature of the water and room temperature is reduced

Question 1188251: A pan of water is brought to a boil and then removed from the heat. Every 5 minutes thereafter the difference between the termperature of the water and room temperature is reduced by 50%.
a) Room temperature is 20 degrees Celcius. Express the temperature of the water as a function of the time since it was removed from the heat.
b) How many minutes does it take for the termperature of the water to reach 30 degree Celcius.
Found 2 solutions by Solver92311, ikleyn:
Answer by Solver92311(821)   (Show Source): You can put this solution on YOUR website!

Please post your Physics problems on a Physics website

John

My calculator said it, I believe it, that settles it

From
I > Ø

Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
A pan of water is brought to a boil and then removed from the heat.
Every 5 minutes thereafter the difference between the temperature
of the water and room temperature is reduced by 50%.
a) Room temperature is 20 degrees Celsius. Express the temperature of the water
as a function of the time since it was removed from the heat.
b) How many minutes does it take for the temperature of the water to reach 30 degree Celsius.
~~~~~~~~~~~~~~~~~

            It is a STANDARD problem on the Newton's law of cooling,
            which is a standard application of logarithms and exponential functions.

            So, it is TOTALLY GOOD ( legal ) for this forum.

I will assume that the boiling temperature is 100 °C (standard for water at normal conditions). Then according to the Newton's cooling law, the temperature of the water at any time moment t after removing from the heat is T(t) = 20 + . This formula is the answer to your first question (a). To answer your second question, write this equation as you read the problem 30 = . Simplify it step by step 30 - 10 = 20 = = = . At this point, the answer is OBVIOUS: = 2, or t = 2*5 = 10 minutes. It is the answer to your second question (b).

Solved and thoroughly explained in all details.

----------------

To see many other similar (and different) cooling problems, look into the lesson
    - Solving problem on Newton Law of cooling
in this site.

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