When a cold drink is taken from a refrigerator, its temperature is 5 ^{\circ}C. After 25 minutes...

Question:

When a cold drink is taken from a refrigerator, its temperature is 5 {eq}^{\circ} {/eq}C. After 25 minutes in a 20 {eq}^{\circ} {/eq}C room its temperature has increased to 10 {eq}^{\circ} {/eq}C. (Round your answer to two decimal places)

When will its temperature be 14 {eq}^{\circ} {/eq}C?

Newton's Law of Heating/Cooling:

The Newton's Law of Heating/Cooling states that the rate of change of the temperature of an object is directly proportional to the difference of its own temperature {eq}T {/eq} and the temperature of its surroundings {eq}T_s {/eq}.

$$\frac{dT}{dt} = - k (T - T_s) $$

where {eq}k {/eq} is the heating/cooling constant of the object. Manipulating and integrating the equation above, the temperature {eq}T {/eq} of an object after some time {eq}t {/eq} when its initial temperature is {eq}T_0 {/eq} is given by the equation:

$$\begin{align*} &T(t) = T_s + ( T_0 - T_s ) e^{-kt} & \text{[Newton's Law of Heating/Cooling]} \end{align*} $$

Answer and Explanation:

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Taken from a refrigerator, the initial temperature of a cold drink is given to be {eq}T_0 = 5^\circ C {/eq}.

After being exposed to a room with...

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What are Heating and Cooling Curves?

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Chapter 6 / Lesson 5
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