In the simple case of an ideal gas, the temperature sets the average kinetic energy through the Boltzmann constant (J/K), but the temperature is not commonly considered "the energy".
Perhaps it would be helpful if the terms "dimensions" and "units" were defined. I am not aware of an interpretation that would make S=k ln(omega) a dimensionless quantity.
Bob L
________________________________________
From: Phys-l <phys-l-bounces@www.phys-l.org> on behalf of John Denker <jsd@av8n.com>
Sent: Tuesday, September 29, 2015 7:24 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] let's define energy
do you see temperature as a sort of energy?
Yes, absolutely. For example, in the expression
dE = T dS (under some conditions)
there is energy on the LHS. The energy on the RHS
comes entirely from the T, not from the dS.