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Atomic and Condensed Matter
Interpretation of temperature in liquids/solids
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[QUOTE="fluidistic, post: 6871728, member: 122352"] I gave you a recipe to compute the entropy increase (over time) in the general case. You can certainly apply it to the case of a bar placed between 2 reservoirs at different temperatures, where the thermal conductivity of the bar is anistropic. We can keep it simple by considering a 2D case and a crystal orientation such that kappa is a 2x2 matrix like so: ##\kappa = \begin{bmatrix} \kappa_{xx} & 0\\ 0 & \kappa_{yy} \end{bmatrix} ## You can quickly get an analytical formula for the general expression for ##T(x,y)## and you'll see that this temperature distribution depends on both ##x## and ##y## and that the thermal gradient doesn't align along ##\hat x##. Now onto the entropy question, the continuity eq. is ##-\dot S =\nabla \cdot \vec J_S=-\nabla \cdot \left( \frac{\kappa}{T} \nabla T \right)##. That's the entropy production. You have everything in hands, and you can work out every details for the problem you set up. As you can see, there is an entropy production due to the thermal gradient, this is why I mentioned that there's an entropy production term due to Fourier's conduction term, earlier in this thread. The "external work being done on the solid" might be the entering heat flux, i.e. energy, into the system. To answer Lord Jescott's question, yes, the driving force is 1/T (or T, depending on your preferred convention). [/QUOTE]
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Interpretation of temperature in liquids/solids
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