# Newton's Law of Cooling: Differential Equations

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Two identical cups of coffee are poured at the same time into two identical cups. Into one cup is added a teaspoon of cream at Tc which is less than room temperature. !0 minutes later the temperature of this coffee is measured.

The second cup is allowed to sit for 10 minutes and then the cream, at Tc, is added to this cup and the temperature measured.

Which cup has the higher temperature?

Ignore radiation losses

Specific heat of cream and coffee is 1

The ambient temperature of the Room is R and is constant

The masses of the coffee cups can be ignored

The amount (mass) of cream and coffee is identical in both cases.

mc = mass of cream, MC = mass of coffee

Using Newton's law of cooling solve the resulting differential equations to find the solution.

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Newton's law of cooling is briefly illustrated in this solution.

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