A thermometer is removed from a room where the temperature is 21° C and is taken outside, where the air temperature is -12° C. After one-half minute the thermometer reads 11° C. What is the reading of the thermometer at t = 1 min? (Round your answer to two decimal places.) °C How long will it take for the thermometer to reach -8° C? (Round your answer to two decimal places.) min

Sol:-

To solve this problem, we can use Newton's law of cooling, which states that the rate of change of the temperature of an object is proportional to the difference between the object's temperature and the temperature of its surroundings.

Let T(t) be the temperature of the thermometer at time t. Then, we have:

dT/dt = k(T - T_s)

where k is a constant of proportionality, T_s is the temperature of the surroundings (in this case, -12° C), and dT/dt is the rate of change of the temperature.