First slide

Radiation

Question

Certain quantity of water cools from $70^{0} C to 60^{0} C in the first 5 minutes and to 54^{0} C$ in the next 5 minutes. The temperature of the surroundings is

Moderate

A

$45^{0} C$
B

$20^{0} C$
C

$42^{0} C$
D

$10^{0} C$

Solution

Newton's law of cooling
$\frac{θ_{1} - θ_{2}}{∆ t} = K [\frac{θ_{1} + θ_{2}}{2} - θ_{0}]$
First $\Rightarrow \frac{70 - 60}{5} = K [65 - θ_{0}]$
$\Rightarrow 2 = K [65 - θ_{0}] - - - - - - (i)$
Next $\Rightarrow \frac{60 - 54}{5} = K [57 - θ_{0}] - - - - - - (ii)$
Dividing (i) and (ii) $\frac{5}{3} = \frac{65 - θ_{0}}{57 - θ_{0}}$
$\Rightarrow 285 - 5 θ_{0} - 195 - 3 θ_{0} \Rightarrow 2 θ_{0} = 90$
$θ_{0} = 45^{0}$

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