Suppose that at time t = 0 an object with temperature T0 isplaced in a room with
Chapter 8, Problem 58(choose chapter or problem)
Suppose that at time \(t=0\) an object with temperature \(T_{0}\) is placed in a room with constant temperature \(T_{a}\). If \(T_{0}<T_{a}\), then the temperature of the object will increase, and if \(T_{0}<T_{a}\), then the temperature will decrease. Assuming that Newton's Law of Cooling applies, show that in both cases the temperature \(T(t)\) at time t is given by
\(T(t)=T_{a}+\left(T_{0}-T_{a}\right) e^{-k t}\)
where k is a positive constant.
Equation Transcription:
Text Transcription:
t=0
T_0
T_a
T_0<T_a
T(t)
T(t)=T_a+(T_0-T_a)e^-kt
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