A liquid is being heated in an oven maintained at a constant temperature of $$ 160^{\circ} \mathrm{C} $$. It may be assumen that the rate of increase of the temperature of the liquid at any particular time $$ t $$ minutes is proportiona to $$ 160- heta $$, where $$ heta^{\circ} \mathrm{C} $$ is the temperature of the liquid at that time. (i) Write down a differential equation connecting $$ heta $$ and $$ t $$. When the liquid was placed in the oven, its temperature was $$ 20^{\circ} \mathrm{C} $$ and 5 minutes later its temperature had risen to $$ 65^{\circ} \mathrm{C} $$. (ii) Find the temperature of the liquid, correct to the nearest degree, after another 5 minutes.

Question

A liquid is being heated in an oven maintained at a constant temperature of $$ 160^{\circ} \mathrm{C} $$. It may be assumen that the rate of increase of the temperature of the liquid at any particular time $$ t $$ minutes is proportiona to $$ 160-	heta $$, where $$ 	heta^{\circ} \mathrm{C} $$ is the temperature of the liquid at that time. (i) Write down a differential equation connecting $$ 	heta $$ and $$ t $$. When the liquid was placed in the oven, its temperature was $$ 20^{\circ} \mathrm{C} $$ and 5 minutes later its temperature had risen to $$ 65^{\circ} \mathrm{C} $$. (ii) Find the temperature of the liquid, correct to the nearest degree, after another 5 minutes.

Ruiz Brooks · Accepted Answer

**Answer:** Problem i Answer: The differential equation is $$\dfrac{dθ}{dt} = k(160 - θ)$$. Problem ii Answer: After another 5 minutes, the temperature of the liquid is approximately $$96^\circ 	ext{C}$$.

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