Newton\'s law of cooling states that the temperature of an object changes at a r

Question

Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of 185 degrees Fahrenheit when freshly poured, and 1.5 minutes later has cooled to 168 degrees in a room at 62 degrees, determine when the coffee reaches a temperature of 123 degrees. Note: the answer is not 15.182 minutes. That's what i got and it was wrong.

Explanation / Answer

I went through the following "mechanics" to show you that this differential can be solved and treated as a simple initial value problem. Solve Newton's Law of Cooling differential for T(t) dT/dt = -k(Tt - Ta) d/dt (Tt - Ta) = dTt/dt - dTa/dt Note that dTa/dt is 0 thus d/dt (Tt - Ta) = dTt/dt Let (Tt - Ta) = T then

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.