A new kind of science
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Exploitation of a real-time computer experiment connected with advanced education of statistical mechanics and thermodynamics allows us to study a commonly occurring phenomenon of heat transfer through a diathermic wall; this wall separates the container into two parts consisting of an ideal gas at different temperatures. The system as a whole is isolated from the surroundigs by very massive border walls. We assume that the walls are rough which introduces the necessary spatial molecular chaos in the system. We study (i) the thermalization process where the temperatures of both parts of the container relax to the same, final one. We found (ii) that the temperature difference relaxes according to the empirical Newton's law of cooling obeyed by real systems. Finally, we confirmed (iii) the law of entropy increase and verified its validity for this small system. We used a simple hybrid molecular dynamics where the scattering of atoms has a random character but between the successive scattering steps the motion of atoms is deterministic.