A cool drink is removed from a refrigerator on a hot summer day and placed in a room whose temperature is ...?

Question

30 degrees Celsius. According to Newton's law of cooling, the temperature of the drink (t) minutes later is given by a function of the form f(t)= 30-(A(e^kt)). Show the rate of change of the temperature of the drink with respect to time is proportional to the difference between the temperature of the room and that of the drink.

Answer 1

f(t) = 30 - Ae^(kt)

f'(t) = - kAe^(kt)

- Ae^(kt) = f(t) - 30

f'(t) = k(f(t) - 30) = - k(30 - f(t))

or, in general,

d(Td)/dt = - k(Tr - Td)