MATH 105 Lecture 30: MATH 105 Lecture 30
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It 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). The law tells us about the instantaneous rate of change of the temperature using a differentiation equation. The equation will give us a function that tracks the complete record of the temperature over time. Equations for newton"s law of cooling dt/dt = -k(t - t a ) T(t) = temperature of the soup at time t (in min) T(0) = t a = initial temperature of the soup = 100 deg. T a = ambient temperature (temp of water in sink) = 5 deg. Given: the rate of change of the temperature dt/dt is (by newton"s law) proportional to the difference between the temperature of the soup t(t) and the ambient temperature t a , giving: dt/dt is proportional to (t - t a )
