Question

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 -

• A. $\frac{7}{4} T$
• B. $\frac{3}{2} T$
• C. $\frac{4}{3} T$
• D. $T$

Answer 1

Answer: (B)

$3T\xrightarrow{t_1 = 10 \; min} 2T \xrightarrow{t_2 = 10 min} T_f$
$T_{0} =T $
$ \left(\frac{3T - 2T}{10}\right) = c_{1} \left(\frac{3T + 2T}{2} - T\right) $ ...(i)
$ \left(\frac{2T - T_{f}}{10}\right) =c_{1}\left(\frac{2T + T_{f}}{2} - T\right) $ ....(ii)
$\frac{Eq.\left(i\right)}{Eq.\left(ii\right)} \Rightarrow \frac{\frac{T}{10}}{\frac{2T -T_{f}}{10}} = \frac{\frac{5T-2T}{2}}{\frac{T_{f}}{2}} $
$ \frac{T}{2T - T_{f}} = \frac{3T}{T_{f}}$
$ T_{f} = 6T - 3T_{f} $
$ 4T_{f} = 6T$
$ T_{f} = \frac{3}{2} T $