Question #342825

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.


1
Expert's answer
2022-05-20T06:48:35-0400

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

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

ln(TTs)=kt+C1ln(T-T_s)=kt+C_1

T=Ts+C2ektT=T_s+C_2e^{kt}

T(0)=Ts+C2

C2=T(0)-Ts

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

T(40)=40+(8040)e0.05ln2x40=200T(40)=40+(80-40)e^{0.05ln2x40}=200


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