Answer to Question #342825 in Differential Equations for Musad

Question

a chip is placed at room temperature of 40°c after minutes its temperature changes from 80c to 60c the proportionallity constant in case is k=0.05 ln2 find temperture of chip after 40 minute.

Answer 1

Recall Newton’s law of cooling: the rate of change in temperature of an object is proportional

to the difference in temperature between the object and its surroundings,

$dT/dt=k(T-T_s)$

$\int ( dT/(T-T_s))=\int k dt$

$ln(T-T_s)=kt+C_1$

$T=T_s+C_2e^{kt}$

T(0)=T_s+C₂

C₂=T(0)-T_s

$T(t)=T_s+(T(0)-T_s)e^{kt}$

$T(40)=40+(80-40)e^{0.05ln2x40}=200$