Question
A body is found to cool from 100°C to 90°C in 5 minutes and from 90°C to 80°C in 6 minutes. Find the temperature of surrounding.
Solution
According to Newton’s law of cooling,
where,
Ta is the average temperature of body, and
T0 is the temperature of surrounding.
When the body cools from 100°C to 90°C, the fall in temperature is 10°C.
Average temperature of the body is 95°C.
Therefore,
...(1)
When the temperature of the body falls from 90°C to 80°C the average temperature of body is 85°C.
Thus,
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...(2)
Dividing (1) by (2), we get
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, is the temperature of the surrounding.
where,
Ta is the average temperature of body, and
T0 is the temperature of surrounding.
When the body cools from 100°C to 90°C, the fall in temperature is 10°C.
Average temperature of the body is 95°C.
Therefore,
...(1) When the temperature of the body falls from 90°C to 80°C the average temperature of body is 85°C.
Thus,
...(2) Dividing (1) by (2), we get
, is the temperature of the surrounding.
