This post is wrong. Thanks to SymplecticMan for the thought experiment demonstrating that a mixture of ideal gases follows a T3/2 law rather than my proposed 1T law. (It’s also different from Newton’s T law.)
I made a pretty but unjustified assumption — that a cooling baking sheet can be modeled as a dynamical system where each possible transition is equally likely and in which heat is transferred in fixed quanta, one at a time. This contradicted Newton’s law, and I got excited when I realized that Newton’s law was merely a first-order approximation.
My mistake was not noticing that Newton’s law is a first-order approximation to any model of cooling where heat transfer increases with temperature difference, so I had not observed any reason to favor my model over any other.
In penance I have acquired a copy of Non-Equilibrium Thermodynamics by de Groot and Mazur, with the intention of eventually reading it.
This post is wrong. Thanks to SymplecticMan for the thought experiment demonstrating that a mixture of ideal gases follows a T3/2 law rather than my proposed 1T law. (It’s also different from Newton’s T law.)
I made a pretty but unjustified assumption — that a cooling baking sheet can be modeled as a dynamical system where each possible transition is equally likely and in which heat is transferred in fixed quanta, one at a time. This contradicted Newton’s law, and I got excited when I realized that Newton’s law was merely a first-order approximation.
My mistake was not noticing that Newton’s law is a first-order approximation to any model of cooling where heat transfer increases with temperature difference, so I had not observed any reason to favor my model over any other.
In penance I have acquired a copy of Non-Equilibrium Thermodynamics by de Groot and Mazur, with the intention of eventually reading it.
see also phonons