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Question

In a room where the temperature is 30C a body cools from 61C to 59C in 4 minutes. The time taken by the body to cool from 51C to 49C will be about :

A
5 minutes
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B
8 minutes
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C
4 minutes
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D
6 minutes
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Solution

The correct option is D 6 minutes
The average temperature of the liquid in the first case
θ1=61+592=60C
Temperature difference from surrounding
θ1θ0=6030=30C
The rate of fall of temperature is
dθ1dt=61C59C4
=24=12C/min
From Newton's law of cooling
12C/min=K(30)K=160.....(i)
In the second case, average temperature
θ2=51+492=50C
Temperature difference with surrounding
θ2θ0=50C30C
=20C
If it takes a time t to cool from 51C to 49C
then dθ2dt=5149t=2Ct
From Newton's law of cooling
2Ct=160×20
t=6 min

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