Activity 1.5.
An object with an initial temperature of \(T_0\) is placed in an environment with a constant temperature \(T_s\) at \(t=0\text{.}\) The time-dependent temperature of the object is given by:
\begin{equation*}
T = T_s + (T_0 - T_s)e^{-kt}
\end{equation*}
where \(k\) is a positive constant known as the thermal diffusivity and depends on the material’s thermal conductivity (\(K\)), specific heat (\(c\)), and density (\(r\)).
Suppose a soda can with thermal diffusivity of \(k = 1.25×10^{-4}\) that was left in the sun has an initial temperature of \(T = 120ºF\) and was then placed in a refrigerator at \(T=38ºF\text{.}\)
To the nearest degree, what is the temperature of the can after three hours?
