Question 896: Thermodynamics & KTG

Question

A metal sphere cools at the rate of $$1.5^{\circ} \mathrm{C} / \mathrm{min}$$ when its temperature is $$80^{\circ} \mathrm{C}$$. At what rate will it cool when its temperature falls to $$50^{\circ} \mathrm{C}$$. [Temperature of surrounding is $$30^{\circ} \mathrm{C}$$]

Accepted Answer

When temperature is $$80^{\circ} \mathrm{C}$$, by Newton's law of cooling, we have
$$1.5=\mathrm{k}\left(\frac{80+30}{2}-30ight)=\mathrm{k}(55-30)=25 \mathrm{~K}$$
When temperature is $$50^{\circ} \mathrm{C}$$, let $$\mathrm{r}$$ be the rate of cooling.
Then
$$\begin{aligned}
& 	ext { Then } \
& r=k\left(\frac{50+30}{2}-30ight)=k(40-30)=10 \mathrm{~K} \
& 	herefore \quad \frac{r}{1.5}=\frac{10}{25} \quad 	herefore r=\frac{10}{25} 	imes 1.5=\frac{3}{5}=0.6^{\circ} \mathrm{C} / \mathrm{min}
\end{aligned}$$

Answer

$$0.9^{\circ} \mathrm{C} / \mathrm{min}$$

Answer

$$0.6^{\circ} \mathrm{C} / \mathrm{min}$$

Answer

$$1.5^{\circ} \mathrm{C} / \mathrm{min}$$

Answer

$$1.2^{\circ} \mathrm{C} / \mathrm{min}$$

Thermodynamics & KTG

A metal sphere cools at the rate of $1.5^{\circ} \mathrm{C} / \mathrm{min} when its temperature is 80^{\circ} \mathrm{C}. At what rate will it cool when its temperature falls to 50^{\circ} \mathrm{C}. [Temperature of surrounding is 30^{\circ} \mathrm{C}$]

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