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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 the next 10 minutes will be:

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$\frac{7}{4} T$

$\frac{3}{2} T$

$\frac{4}{3} T$

$T$

answer is B.

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Detailed Solution

Change in temperature is from 3T to 2T

Time = 10 min

From Newton's law of cooling

$\ln (\frac{3 T - T}{2 T - T}) = K t \ln (2) = K (10)$ for next 10 min $\ln (\frac{2 T - T}{T^{'} - T}) = k (10) \frac{2 T - T}{T^{'} - T} = 2 T^{'} = \frac{3}{2} T$

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