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A body in a room cools from 90°C to 80°C in 5 minutes. the time taken to cool from 70°C to 60°C is (a) Less than 5 minute (b) 5 minute (c) More than 5 minutes (d) Less or more than 5 minutes depending upon the nature of the body

A body in a room cools from 90°C to 80°C in 5 minutes. the time taken to cool from 70°C to 60°C is
(a) Less than 5 minute
(b) 5 minute
(c) More than 5 minutes
(d) Less or more than 5 minutes depending upon the nature of the body

Grade:Upto college level

2 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
3 years ago
Dear student

The answer is option c

Regards
Vikas TU
14149 Points
3 years ago
Initial temperature ( Ti) = 80°C
Final temperature ( Tf) = 50°C
Temperature of the surrounding ( To) = 20°C
t = 5 min
A/C to Newton's law of cooling
Rate of cooling ( dT/dt) = K[ (Ti+Tf)/2 - To]
( Tf - Ti)/t = K[ ( 80 + 50)/2 - 20]
( 80-50)/5 = K[ 65 - 20]
6 = K× 45
K = 6/45 = 2/15
in second condition,
initial temperature ( Ti) = 60°C
Final temperature ( Tf) = 30°C
Time taken for cooling is t
A/C Newton's law of cooling
( 60 - 30)/t = 2/15 [ (60+30)/2 -20]
30/t = 2/15 × 25
30/t = 50/15 = 10/3
t = 9 min
 

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