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A liquid takes 10 minute to cool from 75℃ to 50℃ 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 75℃ to 50℃ how much time will it take to cool from 60℃ to 40℃ temperature is surrounding is 20℃

Grade:11

1 Answers

Arun
25750 Points
6 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 = [(75+50)/2 - 20)]/[(75 - 50)/10]
     = 42.5 / 2.5 = 17
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) * 17
  = 340/30 min
 = 11.33 min
The body takes 11.33 min to cool from 60°C to 40°C. 

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