# Internal energy + entropy for molecule

1. Dec 9, 2015

### tonyjk

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

2. Dec 9, 2015

### Staff: Mentor

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?

3. Dec 9, 2015

### tonyjk

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: Dec 10, 2015
4. Dec 10, 2015

### nasu

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?

5. Dec 11, 2015

### DrDu

In statistical mechanics, there is nothing wrong with defining entropy for a single molecule.

6. Dec 11, 2015

### tonyjk

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?