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Problem
From Newton's Law of Cooling, we can use the differential equation
dT/dt= -k(T-Ts)
where Ts is the surrounding temperature, k is a positive constant, and T is the temperature.
Let [tex]\tau[/tex] be the time at which the initial temperature difference T0-Ts has been reduced by half. Find the relation between k and [tex]\tau[/tex].
Work
I have found the temperature equation for the object to be
T(t) = Ts + (T0-Ts)e-kt
If the initial temperature difference is reduced by half, i tried
T(t) = Ts + 0.5(T0-Ts)e-kt
but couldn't solve it any further. Could someone please shed some light on what i should do next?
From Newton's Law of Cooling, we can use the differential equation
dT/dt= -k(T-Ts)
where Ts is the surrounding temperature, k is a positive constant, and T is the temperature.
Let [tex]\tau[/tex] be the time at which the initial temperature difference T0-Ts has been reduced by half. Find the relation between k and [tex]\tau[/tex].
Work
I have found the temperature equation for the object to be
T(t) = Ts + (T0-Ts)e-kt
If the initial temperature difference is reduced by half, i tried
T(t) = Ts + 0.5(T0-Ts)e-kt
but couldn't solve it any further. Could someone please shed some light on what i should do next?