Newton's Law of Cooling and other applications of differential equations Section 5-M.

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Newton's Law of Cooling and other applications of differential equations Section 5-M

Newton’s Law of Cooling Newton’s Law of Cooling states that the rate of change in the temperature of an object is proportional to the difference between the temperature of the object and the temperature of its surroundings. Cooling; therefore k is negative

Newton’s Law of Cooling

Newton’s Law of Cooling Solve the separable differential equation We get: Where T is the temperature of the object at time t And Ts is the temperature of the surroundings And To is the initial temperature of the object

1. We take a pie out of the oven where the initial temperature is 220°F and set it on the porch to cool to 40°F. 15 minutes later, the temperature of the pie is 180°F. How long until the pie is room temperature (70°F)?

2. A pan of warm water is 46°C it is put in a fridge 2. A pan of warm water is 46°C it is put in a fridge. After 10 minutes its temperature is 39°C. After 10 more minutes the temperature is 33°C. Estimate the temperature of the fridge.

Home Work Use a section header for each of the topics, so there is a clear transition to the audience. Worksheet 5-M