# 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 – unsym Dec 17 '13 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 $dS = \frac{\delta Q}{T}$? – DJBunk Dec 18 '13 at 14:33