Gibbs Paradox Solution by James A Putnam

Dear Akinbo,

Thank you for your interesting questions:

"I think your proposed definition of temperature may help resolve some problems as I have often wondered what the entropy increase would be if temperature was about 0K in the equation, ∆S = ∆E/T. As you noted, "The thermodynamic entropy at a temperature of approximately zero degrees Kelvin is very large". How large can this get?"

The equation applies to an ideal gas. An ideal gas is not complex enough to model the behaviors of real gases. It is the case, though, that as the pressure of a gas approaches zero, the properties of the gas will become very much like those of an ideal gas. There is a limit to how far the ideal gas model can be applied. It does not account for intra-molecular motions. However, even in the real gas case, it is the inter-molecular transfer of kinetic energy that temperature is representative of. If the temperature could be zero, then the rate of transfer of kinetic energy would be zero; however, absolute zero cannot be reached. It cannot exist anywhere in the universe. These are my words. The reason it cannot exist anywhere in the universe is because changes of velocities occur in the universe. So long as there are changes of velocities of objects anywhere, there will always be changes of velocities of objects everywhere. Kinetic energy anywhere cannot be zero for the reason that objects can and do respond immediately to motions of other objects, no matter what the intervening distance is. Theoretical physics will offer a different response.

"Is there any technological application to be derived from such disproportionately large entropy?"

Speaking ideally, an infinite thermodynamic entropy could occur only if motion everywhere ceased. My essay explains why thermodynamic entropy is a measure of time only. It is the time required for kinetic energy to be absorbed at the rate that is directly proportional to temperature. I need to emphasize, that temperature would and should have been that rate. Temperature is not something different from that rate other than its units were established arbitarily. A proportionality constant corrects this problem. The units of the rate of transfer of kinetic energy and the units of temperature should be identical. In my essay it is shown that this always should have been the case. It was the use of a theoretical indefinable unit of degrees for temperature that has blocked understanding what temperature is. In answer to your question, thermodynamic entropy is not a physical something that could be exploited for mechanical purposes. It is a measure of time and time is not available for exploitation.

"Perhaps, your definition of temperature would show the inapplicability of this equation for temperatures tending towards 0K?"

The equation accurately represents what would be the case as the temperature approaches zero, but, only for the transfer of kinetic energy between molecules. It does not pertain to the internal temperature of a molecule. So long as a single gas molecule has particles internally that are changing their velocities then it has a temperature. Vibrational motions of the molecule can be transferred externally to another gas molecule. Even if no heat is added to the gas, as I show in my essay, the gas has an internal thermodynamic entropy and that entropy is not zero so long as molecules change their velocities for any reason.

I will read your essay. Thank you for visiting.

James Putnam

In my recent message to Akinbo, I stated:

"It was the use of a theoretical indefinable unit of degrees for temperature that has blocked understanding what temperature is."

In this message I add that: The most important finding is that the choice of the theoretical indefinable units of kilograms for mass is responsible for blocking an understanding of what mass is. Mass is the inverse representation of the acceleration of light. Particles of matter are individual centers of accelerations of light. The 'light' that is being accelerated is photons.

The early theoretical error of the choice to make mass an arbitrarily indefinable property with an arbitrarily indefinable unit is corrected by making mass a defined property. It is now defined using only the properties of the empirical evidence from which its existence was inferred. Higher level theory is greatly dependent upon the current indefinable nature of mass. Correcting the definition of mass changes physics theory greatly. That is what my essays have been about demonstrating.

James Putnam