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a body takes 8 mins to cool from 90°C to 80°C in a surrounding of temperature 25°C .the time taken by it to cool from 80°C to 70°C in the same surrounding is

a body takes 8 mins to cool from 90°C to 80°C in a surrounding of temperature 25°C .the time taken by it to cool from 80°C to 70°C in the same surrounding is

Grade:11

1 Answers

Arun
25763 Points
3 years ago
Dear Student
 
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 =  [(90
+80)/2   -  25)]/[(90 - 80)/8]
         = 48

Substituting T1 = 80 and T2 = 70 and T0 = 25  (all in °C) in Eq. (1), we get

mc (80 - 70)/t = k [(80+ 70)/2   -  25)] 
10 mc/t  = 50 k
t =  mc/(5k) 
  = 48/5
  = 9.6 min

The body takes 9.6 min to cool from 80°C to 70 °C.  
 
Regards
Arun (askIITians forum expert)

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