SOLUTION: A bottle of soda at room temperature (72 F) is placed in a refrigerator where the temperature is 44 F. After half an hour, the soda has cooled to 61 F. What is the temperature of t

Question 1140209: A bottle of soda at room temperature (72 F) is placed in a refrigerator where the temperature is 44 F. After half an hour, the soda has cooled to 61 F. What is the temperature of the soda after another half hour?
Found 3 solutions by Shin123, MathTherapy, greenestamps:
Answer by Shin123(626)   (Show Source): You can put this solution on YOUR website!
During the first half hour, the temperature of the soda decreased by 72-61=11 F. So by the next half hour, the temperature of the soda would be 61-11= 50 F.
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

A bottle of soda at room temperature (72 F) is placed in a refrigerator where the temperature is 44 F. After half an hour, the soda has cooled to 61 F. What is the temperature of the soda after another half hour?

50^o is WRONG!
Correct answer: 60 minutes or 1 hour after being placed in the refrigerator, and using Newton's Law of Cooling, the soda will have a temperature of:
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

I don't know why anyone would say that the temperature of the soda will continue to cool by 11 degrees per hour, when the temperature of the refrigerator is 44 degrees....

Newton's law of cooling says that the rate of cooling is proportional to the difference between the two temperatures.

Initially, the difference between the temperatures of the soda and refrigerator was 28 degrees.

In the first half hour, the temperature of the soda decreased from 72 to 61 degrees, a decrease of 11 degrees.

This means that from the beginning to the end of each half hour, the temperature will decrease by 11/28 of the difference between the two temperatures at the beginning of the half hour.

Take the difference between the temperatures of the soda and the refrigerator at the beginning of the second half hour and multiply it by 11/28. That will give you the amount of cooling in the second half hour; subtract that from the temperature at the beginning of the second half hour to find the temperature of the soda at the end of the second half hour.

You will get the answer shown by the other tutor.
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