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\( \frac { d T } { d t } = - k ( T - 20 ) \)

Ask by Gordon Salazar. in Colombia
Mar 15,2025

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La solución de la ecuación diferencial \( \frac{dT}{dt} = - k (T - 20) \) es: \[ T(t) = 20 + A e^{-kt} \] donde \(A\) es una constante determinada por las condiciones iniciales.

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Bonus Knowledge

This charming little equation describes Newton's Law of Cooling! It tells us that the rate of change of temperature \( T \) over time \( t \) is proportional to the difference between the temperature of the object and the surrounding temperature, which is set at 20 degrees in this case. Essentially, if something is hotter than its environment, it cools down; if it's colder, it warms up. It's like a warm cookie trying to adjust to the room temperature! In real-world scenarios, this concept is used in many fields, including cooking, meteorology, and even criminal investigations! For example, if a baked good comes out of the oven and is initially hot, it will cool down as it sits in a cooler environment. Chefs can time their recipes using this principle, ensuring that their delicious creations are served at just the right temperature. Similarly, investigators can use the cooling of a body to estimate the time of death, revealing clues from the temperature changes.

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