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A body cools from 75 °C to 65 °C in 5.0 minutes in a room at 25 °C.

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A body cools from $75\ ^\circ\text{C}$ to $65\ ^\circ\text{C}$ in $5.0$ minutes in a room at $25\ ^\circ\text{C}$ . Using the average excess temperature, how long does it take to cool from $65\ ^\circ\text{C}$ to $55\ ^\circ\text{C}$ ?

Need a reminder? The key ideaShow

Newton's law of cooling: $\dfrac{dT}{dt} = -k(T - T_0)$ , so $T = T_0 + (T_s - T_0)e^{-kt}$ . Over a short interval, the rate is in proportion to the average excess over the surroundings.

The worked solution

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← A cup of coffee cools from 88 °C to 78 °C in 3.5 minutes in a room at 22 °C.A body is 20 K warmer than the room. It cools by Newton's law, and its excess falls to 10 K in 6.0… →

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