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A differential equation for the temperature ' $\mathrm{T}$ ' of a hot body as a function of time, when it is placed in a both which is held at a constant temperature of $32^{\circ} \mathrm{F}$, is given by (where $\mathrm{k}$ is a constant of proportionality)
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The correct answer is:
$\frac{\mathrm{dT}}{\mathrm{dt}}=\mathrm{k}(\mathrm{T}-32)$
The temperature $\mathrm{T}$ of the body will decrease with time. The body is kept in a bath of temperature $32^{\circ} \mathrm{F}$.
$$
\begin{aligned}
& \therefore \frac{\mathrm{dT}}{\mathrm{dt}} \alpha-(\mathrm{T}-32) \\
& \Rightarrow \frac{\mathrm{dT}}{\mathrm{dt}}=-\mathrm{k}(\mathrm{T}-32)
\end{aligned}
$$
$$
\begin{aligned}
& \therefore \frac{\mathrm{dT}}{\mathrm{dt}} \alpha-(\mathrm{T}-32) \\
& \Rightarrow \frac{\mathrm{dT}}{\mathrm{dt}}=-\mathrm{k}(\mathrm{T}-32)
\end{aligned}
$$
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