# How do you define a reversible path for general processes?

The equation $dS = \frac{\delta Q}{T}$ is only defined for a reversible path. Given a irreversible path we typically calculate the entropy by choosing a reversible path from the same initial to final state. All examples I have seen involves some sort of reservoir that loses entropy such that $\Delta S_{system} =\Delta S_{original}+\Delta S_{res}= 0$ for the total system in the reversible case, where by `original' I mean the system that was originally in consideration that I had to attached a reservoir to in order to find a reversible path.

My question is this:

(1) In the scheme of attaching a reservoir to our system, how would we generally find a reversible path to calculate the change in entropy for a system?

(2) Depending on the answer to the above: Specifically, if I mix a bunch of liquids together (clearly irreversible) what is the reversible path I could use to find the change in entropy for the irreversible case, and does it involve a reservoir?

• The first equation you written is defined for any (sub)system, not path. You can then find the total change in entropy by summing all dS for the subsystem Dec 17, 2013 at 19:21
• hwlau - I am not sure what you mean by "...(sub)system, not path..." - Since $\delta Q$ is a path dependent quantity, don't I have to, in practice, specify what path I am taking in order to use the equation $dS = \frac{\delta Q}{T}$? Dec 18, 2013 at 14:33