Question

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State and explain Newton's Law Of Cooling.

Answer 1

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here is ur ans...

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Newton's Law Of Cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature (i.e. the temperature of its surroundings).

$\frac{dt}{dt} = \: - k \: (t - to)$
Newton's Law makes a statement about an instantaneous rate of change of the temperature. We will see that when we translate this verbal statement into a differential equation, we arrive at a differential equation. The solution to this equation will then be a function that tracks the complete record of the temperature over time.

$\frac{dt}{dt} = - k(t - to) \\ \\ = > \ l \: \frac{dt}{t - to} \: = - l \: kdt \\ \\ = > ln(t - to) = - kt + ln(c) \\ \\ = > t - to = c \: {e}^{ - kt} \\ \\ = > t = to + c \: {e}^{ - kt}$



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