First slide

Radiation

Question

A spherical object cools from $80^{0} C t o 64^{0} C i n 5 \min .$ The same body cools from $80^{0} C t o 52^{0} C i n 10 \min .$ Then temperature of the surrounding is

Easy

A

$18^{0} C$
B

$24^{0} C$
C

$22^{0} C$
D

$16^{0} C$

Solution

(2)
According to Newton's Law of cooling,
$\begin{array}{l} \frac{80 - 64}{5} = K (\frac{80 + 64}{2} - θ_{0}) ..... (1) \\ \frac{80 - 52}{10} = K (\frac{80 + 52}{2} - θ_{0}) ..... (2) \\ (1) \div (2) \Rightarrow \frac{3.2}{2.8} = \frac{72 - θ_{0}}{66 - θ_{0}} \Rightarrow θ_{0} = 24^{0} C \end{array}$

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