Knowing that $$ dT/dt = k(T-Ts) $$
How can i go backward in the question to find the cold room's temperature?
The answers down are wrong, the first answer is 6 and the second is 13.
How can i solve this question using newton's law of cooling and warming?
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calculus
ordinary-differential-equations
exponential-function
education
mathematical-physics
1 Answers
1
Newton's law of cooling says when the temperature of a body $T$ decrease proportional to difference between body temperature and room temperature $T_s$, $T$ will decrease till body temperature and room temperature be equal. Thus with this description $$\frac{dT}{dt}=k(T-T_s)~~~~~~~,~~~~~~~T>T_s~,~~~~k<0$$ and solving this equation $$\frac{dT}{T-T_s}=kdt$$ $$\int\frac{dT}{T-T_s}=\int kdt$$ $$\ln(T-T_s)=kt+C$$ If in time $t=0$ the room's temperature be $T_0$ so $$T=T_s+(T_0-T_s)e^{kt}$$