A block of metal is heated to a temperature much higher than the room temperature and allowed to cool in a room free from air currents. Which of the following curves correctly represents the rate of cooling ?

Concept Videos :-

#52-Newton's Law of Cooling
#54-Solved-Examples-25
#56-Solved-Examples-26

Concept Questions :-

Newton's law of cooling

(b) According to Newton's law of cooling

Rate of cooling ∝ Temperature difference
$⇒-\frac{\mathrm{d\theta }}{\mathrm{dt}}\propto \left(\mathrm{\theta }-{\mathrm{\theta }}_{0}\right)⇒-\frac{\mathrm{d\theta }}{\mathrm{dt}}=\mathrm{\alpha }\left(\mathrm{\theta }-{\mathrm{\theta }}_{0}\right)$  ($\mathrm{\alpha }$= constant)
${\int }_{{\mathrm{\theta }}_{1}}^{\mathrm{\theta }}\frac{d\mathrm{\theta }}{\left(\mathrm{\theta }-{\mathrm{\theta }}_{0}\right)}=-\mathrm{\alpha }{\int }_{0}^{\mathrm{t}}\mathrm{dt}⇒\mathrm{\theta }={\mathrm{\theta }}_{0}+\left({\mathrm{\theta }}_{i}-{\mathrm{\theta }}_{0}\right){\mathrm{e}}^{-\mathrm{\alpha t}}$
This relation tells us that, temperature of the body varies exponentially with time from ${\mathrm{\theta }}_{\mathrm{i}}$ to ${\mathrm{\theta }}_{0}$
Hence graph (b) is correct.

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