Question

A body cools from 80℃ to 50℃ in 5min. calculate the time it takes to cool from 60℃ to 30℃. The temp. of surrounding is 20℃.
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Answer 1

A body cools from 80℃ to 50℃ in 5min. calculate the time it takes to cool from 60℃ to 30℃. The temp. of surrounding is 20℃.

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Answer 2

A body cools from 80℃ to 50℃ in 5min. calculate the time it takes to cool from 60℃ to 30℃. The temp. of surrounding is 20℃.

Good question,

Here is your perfect answer!

1st case,

t(i)1 = 80°C,

t(f)1 = 50°C,

Time = 5 min,

By Newton's law of cooling,

Constant taken as x.

=) x[(80-50)2 - To]

=) ( 80-50)/5 = x( 65 - 20)

=) 6 = x(45)

=) 6/45 = x

=) x = 2/15,

2nd case,

t(i)2 = 60°C,

t(f)2 = 30° C,

Time =?

x = 2/15,

Applying newton's cooling law,

=) ( 60 - 30)/t = 2/15 { (60+30)/2 - 20}

=) 30/t = 2/15 * 25

=) 30*15/50 = t

=) 9 minutes.