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A liquid takes 10 minute to cool from 80℃ to 40℃ how much time will it take to cool from 60℃ to 40℃ temperature is surrounding is 20℃

A liquid takes 10 minute to cool from 80℃ to 40℃ how much time will it take to cool from 60℃ to 40℃ temperature is surrounding is 20℃

Grade:11

1 Answers

Arun
25763 Points
3 years ago
Dear Amar
 
According to Newton's law of cooling, we have
mc (T1 - T2)/t = k [(T1 + T2)/2   -  T0)]        ---------------(1)
mc/k  =   [(T1 + T2)/2   -  T0)]/[(T1 - T2)/t]
mc/k =  [(80
+40)/2   -  20)]/[(80- 40)/10]
         = 60 / 4 = 15
Substituting T1 = 60 and T2 = 40 and T0 = 20  (all in °C) in Eq. (1), we get
mc (60 - 40)/t = k [(60+ 40)/2   -  20)] 
20 mc/t  = 30 k
t = 20 mc/(30k) 
  = (20/30) * 15
  = 300/30 min
 = 10 min
The body takes 10 min to cool from 60°C to 40 °C.

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