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An object at temperature T0 is removed from an oven at time t = 0 and left to cool in surroundings at temperature Ts. Using Newton's law of cooling, write its temperature T as a function of time t (k > 0).

1. T = Ts - (T0 + Ts)e^(-kt)
2. T = Ts + (T0 + Ts)e^(-kt)
3. T = Ts + (T0 - Ts)e^(-kt)
4. T = Ts - (T0 - Ts)e^(-kt)

Correct answer: T = Ts + (T0 - Ts)e^(-kt)

Solution

Integrating dT/dt = -k(T - Ts) gives T - Ts = (T0 - Ts)e^(-kt), i.e. T = Ts + (T0 - Ts)e^(-kt).

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