Only one of them actually corresponds with temperature for all objects. They are both equal for one subclass of idealized objects, in which case the “average kinetic energy” definition follows from the the entropic definition, not the other way around. All I’m saying is that it’s worth emphasizing that one definition is strictly more general than the other.
Average kinetic energy always corresponds to average kinetic energy, and the amount of energy it takes to create a marginal amount of entropy always corresponds to the amount of energy it takes to create a marginal amount of entropy. Each definition corresponds perfectly to itself all of the time, and applies to the other in the case of idealized objects. How is one more general?
Two systems with the same “average kinetic energy” are not necessarily in equilibrium. Sometimes energy flows from a system with lower average kinetic energy to a system with higher average kinetic energy (eg. real gases with different degrees of freedom). Additionally “average kinetic energy” is not applicable at all to some systems, eg. ising magnet.
I just mean as definitions of temperature. There’s temperature(from kinetic energy) and temperature(from entropy). Temperature(from entropy) is a fundamental definition of temperature. Temperature(from kinetic energy) only tells you the actual temperature in certain circumstances.
Because one is true in all circumstances and the other isn’t? What are you actually objecting to? That physical theories can be more fundamental than each other?
I admit that some definitions can be better than others. A whale lives underwater, but that’s about the only thing it has in common with a fish, and it has everything else in common with a whale. You could still make a word to mean “animal that lives underwater”. There are cases where where it lives is so important that that alone is sufficient to make a word for it. If you met someone who used the word “fish” to mean “animal that lives underwater”, and used it in contexts where it was clear what it meant (like among other people who also used it that way), you might be able to convince them to change their definition, but you’d need a better argument than “my definition is always true, whereas yours is only true in the special case that the fish is not a mammal”.
The distinction here goes deeper than calling a whale a fish (I do agree with the content of the linked essay).
If a layperson asks me what temperature is, I’ll say something like, “It has to do with how energetic something is” or even “something’s tendency to burn you”. But I would never say “It’s the average kinetic energy of the translational degrees of freedom of the system” because they don’t know what most of those words mean. That latter definition is almost always used in the context of, essentially, undergraduate problem sets as a convenient fiction for approximating the real temperature of monatomic ideal gases—which, again, is usually a stepping stone to the thermodynamic definition of temperature as a partial derivative of entropy.
Alternatively, we could just have temperature(lay person) and temperature(precise). I will always insist on temperature(precise) being the entropic definition. And I have no problem with people choosing whatever definition they want for temperature(lay person) if it helps someone’s intuition along.
What do you mean by “true”? They both can be expressed for any object. They are both equal for idealized objects.
Only one of them actually corresponds with temperature for all objects. They are both equal for one subclass of idealized objects, in which case the “average kinetic energy” definition follows from the the entropic definition, not the other way around. All I’m saying is that it’s worth emphasizing that one definition is strictly more general than the other.
Average kinetic energy always corresponds to average kinetic energy, and the amount of energy it takes to create a marginal amount of entropy always corresponds to the amount of energy it takes to create a marginal amount of entropy. Each definition corresponds perfectly to itself all of the time, and applies to the other in the case of idealized objects. How is one more general?
Two systems with the same “average kinetic energy” are not necessarily in equilibrium. Sometimes energy flows from a system with lower average kinetic energy to a system with higher average kinetic energy (eg. real gases with different degrees of freedom). Additionally “average kinetic energy” is not applicable at all to some systems, eg. ising magnet.
I just mean as definitions of temperature. There’s temperature(from kinetic energy) and temperature(from entropy). Temperature(from entropy) is a fundamental definition of temperature. Temperature(from kinetic energy) only tells you the actual temperature in certain circumstances.
Why is one definition more fundamental than another? Why is only one definition “actual”?
Because one is true in all circumstances and the other isn’t? What are you actually objecting to? That physical theories can be more fundamental than each other?
I admit that some definitions can be better than others. A whale lives underwater, but that’s about the only thing it has in common with a fish, and it has everything else in common with a whale. You could still make a word to mean “animal that lives underwater”. There are cases where where it lives is so important that that alone is sufficient to make a word for it. If you met someone who used the word “fish” to mean “animal that lives underwater”, and used it in contexts where it was clear what it meant (like among other people who also used it that way), you might be able to convince them to change their definition, but you’d need a better argument than “my definition is always true, whereas yours is only true in the special case that the fish is not a mammal”.
The distinction here goes deeper than calling a whale a fish (I do agree with the content of the linked essay).
If a layperson asks me what temperature is, I’ll say something like, “It has to do with how energetic something is” or even “something’s tendency to burn you”. But I would never say “It’s the average kinetic energy of the translational degrees of freedom of the system” because they don’t know what most of those words mean. That latter definition is almost always used in the context of, essentially, undergraduate problem sets as a convenient fiction for approximating the real temperature of monatomic ideal gases—which, again, is usually a stepping stone to the thermodynamic definition of temperature as a partial derivative of entropy.
Alternatively, we could just have temperature(lay person) and temperature(precise). I will always insist on temperature(precise) being the entropic definition. And I have no problem with people choosing whatever definition they want for temperature(lay person) if it helps someone’s intuition along.