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A body cools in 7 minutes from 60^(@)C ...

A body cools in 7 minutes from `60^(@)C` to `40^(@)C`. What will be its temperature after the next 7 minutes? The temperature of the surroundings is `10^(@)C`.

Text Solution

Verified by Experts

In the First case,
`T_1=60"^(@)C,T_2=40"^(@)CT_0=10"^(@)C`,t=7 min From In`((T_1-T_0)/(T_2-T_0))` =kt
we get
In `((60-10)/(40-10))=7k`
In `5/3=7k`
In the Second case
If T is the temperature after next 7 min ,`T_1=40"^(@)C,T_2=T,T_0=10"^(@)C`,t=7 min
In `((40-10))/((T-10))=7 k`
In`(30)/(T-10)=7k`
From equation (i) & (ii)
In`5/3`=In`(30)/(T-10)`
`5/3`=`(30)/(T-10)`
T=`28"^(@)C`
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