The rate at which a substance cools in moving air, is proportional to the difference between the temperature of the substance and that of air. The temperature of air is 290 K and the substance cools from 370 K to 330 K in 10 minutes. Then the time to cool the substance upto 295 K is

Step-by-step solution

Newton's Law of Cooling gives the rate of temperature change proportional to the difference from ambient temperature T_a = 290 K : dT dt = -k(T - 290) Separating variables and integrating yields the general solution: dT T - 290 = -k dt |T - 290| = -kt + CT(t) = 290 + Ae^ -kt The initial condition T(0) = 370 determines the constant A = 80 , giving the temperature function: T(t) = 290 + 80e^ -kt Using the condition that T decreases from 370 K to 330 K in 10 minutes: 330 = 290 + 80e^ -10k e^ -10k = 1 2 To find when T