I am currently trying to get my head around the concept of entropy. One way to understand it is that it can be related to the number of available energy levels in a system.
From what I read, the availability of energy levels in a system:
increase with an increase in the system volume by bringing energy levels closer
increase with an increase in the system temperature by increasing available energy to reach more levels
decrease with an increase in the system pressure by making energy levels further apart
I am currently interested in an example of adiabatic reversible compression and expansion.
Since the process is adiabatic, I know that no heat is exchanged with the surroundings and that therefore there is no entropy transfer to/from the system.
Since the process is reversible then no entropy is generated ... and this is where I'm unsure ... I know that the volume of my compressor doesn't change, so that volume doesn't contribute to changes in availability of energy levels within my compressor (system). I know that both my pressure and temperature increase though and that each have an opposite effect on the availability of energy levels within the system. Therefore I assume that the effects of both cancel out and that overall the availability of energy levels within the system doesn't change and that no entropy is generated within the system. If I am correct in my understanding of the process, I can't find anywhere the equation which shows that the increase in pressure and temperature cancel each other out when it comes to generating entropy.
There is a lot about the $dS = \frac{dQ}{T}$ which is about the entropy transfer across the system boundaries but I can't find much about the entropy generation.
