First slide

Radiation

Question

A body which is initially at $80^{0} C cools to 64^{0} C in 5 \min and to 52^{0} C in 10 \min .$ The temperature of the surrounding should be

Moderate

A

$16^{0} C$
B

$26^{0} C$
C

$36^{0} C$
D

$40^{0} C$

Solution

Using Newton's law of cooling
$\frac{∆ θ}{∆ t} = K [θ_{av} - θ_{0}]$
$(\frac{θ_{1} - θ_{2}}{t}) = K [\frac{θ_{1} + θ_{2}}{2} - θ_{o}]$
In the 1st case, $\frac{80 - 64}{5} = K [\frac{80 + 64}{2} - θ_{o}]$
Or 3.2 = K[72- $θ_{0}$ ]-------(i)
In the 2nd case, $\frac{64 - 52}{5} = K [\frac{64 - 52}{2} - θ_{0}]$
or 2.4 = K( ${58-θ}_{0}$ ) ------(ii)
From (i) by (ii), we get $\frac{3.2}{2.4} = \frac{72 - θ_{0}}{58 - θ_{0}}$
Or $185.6 - 3.2 θ_{0} = 172.8 - 2.4 θ_{0} or θ_{0} = 16^{0} C$

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