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  4. A body takes 4 min. to cool from 61° C to 59° C. If the temperature of the surroundings is 30° C, the time taken by the body to cool from 51° C to 49° C is :

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Q. A body takes $4\, \min$. to cool from $61^{\circ} C$ to $59^{\circ} C$. If the temperature of the surroundings is $30^{\circ} C$, the time taken by the body to cool from $51^{\circ} C$ to $49^{\circ} C$ is :

JEE MainJEE Main 2021Thermal Properties of Matter

Solution:

$\frac{\Delta T}{\Delta t}=K\left(T_{t}-T_{s}\right)$
$T_{t}=$ average temp
$T_{S}=$ surrounding temp.
$\frac{61-59}{4}=K\left(\frac{61+59}{2}-30\right)$ ...(1)
$\frac{51-49}{t}=K\left(\frac{51+49}{2}-30\right)$ ...(2)
Divide (1) & (2)
$\frac{t}{4}=\frac{60-30}{50-30}=\frac{30}{20}$
so, $t=6$ minutes