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From my heat transfer textbook by Cengel and Ghajar, they propose that you use the average thermal conductivity value as you specified in your last equation: $k_{avg} = k(T_{avg}) = k_0(1+\beta(T_a+T_b)/2)$ where $\beta$ and $k_0$ are material properties, assuming that the material thermal conductivity follows a linear function w.r.t temperature. You ...


The traditional method is to use a magnetic stirrer However, what are your dimensions? You might also be able to create something along similar lines by wrapping a coil around the containers.


based on casual observation, believes that coffee will cool faster than ordinary hot tap water Let's revisit the "casual observation" part. Are the initial conditions the same? Water from a kettle will usually be hotter than from a coffee machine. And we tend to do things to coffee that we don't do to water, like add 10% of another liquid (milk) at low ...


Internal Energy = Heat - Work, or U = Q - W. By definition an adiabatic process has constant heat, so when finding the rate of change of each in a process by taking the time derivative: dU = dQ(0) - dW Q goes to zero, and U = W.

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