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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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A body is $20\ \text{K}$ warmer than the room. It cools by Newton's law, and its excess falls to $10\ \text{K}$ in $6.0$ minutes. How long until the excess is $5\ \text{K}$ ? What is the excess after $9.0$ minutes?

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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