First slide

Radiation

Question

The initial temperature of a body is $80^{0} C$ . If its temperature falls to $64^{0} C in 5 minutes and in n e x t 10 minutes to 52^{0}$ . Find the temperature of surrounding.

Moderate

A

$26^{0} C$
B

$60^{0} C$
C

$36^{0} C$
D

$49^{0} C$

Solution

According to Newton's law $\frac{θ_{1} - θ_{2}}{t} = k [\frac{θ_{1} + θ_{2}}{2} - θ_{0}]$
Initially, $\frac{(80 - 64)}{5} = K (\frac{80 + 64}{2} - θ_{0})$
$\Rightarrow 3.2 = K [72 - θ_{0}] - - - - - - - (i)$
Finally, $\frac{(64 - 52)}{10} = K [\frac{64 + 52}{2} - θ_{0}]$
$\Rightarrow 1.2 = K [58 - θ_{0}] - - - - - - (ii)$
On solving equation (i) and (ii) $θ_{0} = 49^{0} C$

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