02 - Time for the thermometer reading to drop to within half degree of the air temperature

Problem 02
A thermometer reading 75 degree Fahrenheit is taken out where the temperature is 20 degree Fahrenheit. The thermometer reading is 30 degree Fahrenheit 4 minutes later. Find the time (in minutes) taken for the reading to drop from 75 degree Fahrenheit to within half degree of the air temperature.

Elementary Applications

Newton's Law of Cooling

Newton's Law of Cooling states that the temperature of a body changes at a rate proportional to the difference in temperature between its own temperature and the temperature of its surroundings.

We can therefore write

$\dfrac{dT}{dt} = -k(T - T_s)$

T = temperature of the body at any time, t
Ts = temperature of the surroundings (also called ambient temperature)
To = initial temperature of the body
k = constant of proportionality