Internal energy + entropy for molecule

AI Thread Summary
Internal energy can theoretically be defined for a single molecule, but entropy is typically defined for a system of many molecules. The discussion explores whether entropy can also be defined for a single molecule, given that temperature is derived from changes in internal energy and entropy. It is clarified that while internal energy can describe individual molecules, the average kinetic energy aligns with the Boltzmann distribution. The relationship between the temperature of a single molecule and macroscopic temperature remains a point of inquiry, emphasizing the connection between microscopic and macroscopic thermodynamic properties. The conversation highlights the nuances of applying statistical mechanics to individual particles versus bulk systems.
tonyjk
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Hello,
Internal energy can be defined theoretically for one molecule (U = 1/2 Kb T) for example but entropy is defined for a system thus for many molecules. Then we define temperature equal to δU / δS but here U can be defined for one molecule, so S can also be defined for one molecule? How?

Thank you
 
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tonyjk said:
Hello,
Internal energy can be defined theoretically for one molecule (U = 1/2 Kb T) for example but entropy is defined for a system thus for many molecules. Then we define temperature equal to δU / δS but here U can be defined for one molecule, so S can also be defined for one molecule? How?

Thank you
Do you really feel that the equation you presented for U describes the kinetic energy of each and every molecule of an ideal gas, or is it just the average kinetic energy over all the molecules, consistent with the Boltzman distribution?
 
Chestermiller said:
Do you really feel that the equation you presented for U describes the kinetic energy of each and every molecule of an ideal gas, or is it just the average kinetic energy over all the molecules, consistent with the Boltzman distribution?
No like I said U can theoretically describe both. For example if U can describe one molecule thus the temperature can describe one molecule. So S can describe one molecule? Then if S cannot describe one molecule, a temperature cannot describe one molecule, so there is a contradiction in the U defintion for one molecule
 
Last edited:
The average number of children per family in the US was 2.7 in 1961.
Can you say that any specific family had 2.7 children?
 
In statistical mechanics, there is nothing wrong with defining entropy for a single molecule.
 
DrDu said:
In statistical mechanics, there is nothing wrong with defining entropy for a single molecule.
Great. So how the temperature of one molecule in statistical mechanics is related to macroscopic temperature (T= dU/dS) of a volume containing this molecule and many others?
 

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