# A body cools from a temperature 3T to 2T in 10 minutes. The room temperature is T. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be Option 1) Option 2) Option 3) Option 4) T

As we learnt in

When body Cools by Radiation from theta1 degree c to theta two degree c in time t -

$\left[\frac{\theta_{1}-\theta_{2}}{t} \right ]=k\left[\frac{\theta_{1}+\theta_{2}}{2}-\theta_{0} \right ]$

- wherein

$\theta_{av}=\frac{\theta_{1}+\theta_{2}}{2}$

From newton's law of cooling

$\\ \frac{3T-2T}{10}=K.(\frac{3T+2T}{2}-T)=\frac{3}{2}KT$

$\frac{T}{10}=\frac{3KT}{2}\ \: \: \: \:or\: \: \: \: K=\frac{1}{15}\ \: \: \: ..........(1)$

Let us say temperature after 10 minutes become T1

Then $\frac{2T-T_{1}}{10}=K\left [ \frac{2T+T_{1}}{2}-T \right ]$

$\\ \frac{2T-T_{1}}{10}=\frac{1}{15}(\frac{T_{1}}{2})\\ or\ \: \: 6T-3T_{1}=T_{1}\ \: \: \: or\ \: \: T_{1}=\frac{3}{2}T$

Option 1)

This solution is incorrect

Option 2)

This solution is correct

Option 3)

This solution is incorrect

Option 4)

T

This solution is incorrect

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