Q104 / 180 · NEET 2016 (Phase 2) · Physics

A body cools from a temperature $3 T$ to $2 T$ 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
$\frac{7}{4} T$
Correct answer
B
$\frac{3}{2} T$
C
$\frac{4}{3} T$
D
$T$

Solution

\frac{T_{1} - T_{2}}{∆ t} = K (\frac{T_{1} + T_{2}}{2} - T_{0})

\frac{3 T - 2 T}{10} = K (2.5 T - T)

\Rightarrow \frac{T}{10} = K (1.5) T

K = \frac{1}{15}

Now,

\frac{2 T - x}{10} = K (\frac{2 T + x}{2} - T)

Solving

x = \frac{3 T}{2}

Hence, the correct answer is option: 'B'.

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