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A liquid takes 10 minute to cool from 70℃ 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 70℃ to 50℃ how much time will it take to cool from 60℃ to 40℃ temperature is surrounding is 20℃

Grade:11

2 Answers

HARDIK
6 Points
3 years ago
APPLYING NEWTON’S LAW OF MOTION,
WE GET,
(70-50)/(10.60)=K((70+50)/2-20)            ........(1)
(60-40)/T= K((60+40)/2-20)                 ........(2)
EQN (1)/EQN.(2)
T/(10.60)=40/30
T = 80 SECONDS.

REGARDS
HARDIK BAWEJA
 
NOTE: PLEASE CHECK ANY CALCULATION ERROR AND ASK AGAIN IF NOT CLEAR...
ALL THE BEST!!
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 = [(70+50)/2 - 20)]/[(70 - 50)/10]
        = 60 / 2 = 30
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) * 30
  = 600 /30 min
 = 20 min
The body takes 20 min to cool from 60°C to 40 °C. 

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