First slide

Radiation

Question

A pan filled with hot food cools from 94⁰C to 86⁰C in 2 min. When the room temperature is at 20⁰C, the time taken to cool from 71⁰C to 69⁰C is

Moderate

A

50 s
B

40 s
C

38 s
D

42 s

Solution

From the Newton's law of cooling,
$\frac{θ_{1} - θ_{2}}{t} \propto (\frac{θ_{1} + θ_{2}}{2} - θ_{0})$
where, $θ_{0}$ = temperature of surrounding
$∴ \frac{94 - 86}{t_{1}} \propto (\frac{94 + 86}{2} - 20)$
$\frac{8}{t_{1}} \propto (70)$ …(i)
and $\frac{71 - 69}{t_{2}} \propto (\frac{71 + 69}{2} - 20)$
$\frac{2}{t_{2}} \propto 50$ …(ii)
On dividing Eq (i) by Eq (ii), we get
$\frac{t_{2}}{t_{1}} = \frac{70}{50 \times 4} \Rightarrow t_{2} = \frac{70 \times 2}{50 \times 4}$
$\Rightarrow t_{2} = 0.7 \min \Rightarrow t_{2} = 42 s$

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