A metal rod is heated in a furnace and then left to cool in air at 25 °C
MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations
Problem
A metal rod is heated in a furnace and then left to cool in air at 25 °C. At the instant it is placed in the air, the rod’s temperature is 180 °C. After 15 minutes its temperature has fallen to 100 °C.
(i) Determine the constant k (in min−1) governing the cooling of the rod.
(ii) Using this value of k, calculate the additional time required for the rod to cool from 100 °C to 40 °C.
(iii) Find the total time, counted from the moment the rod was removed from the furnace, at which its temperature will first reach 30 °C.