Chemistry - entropy calculation in an irreversible process

Quantities such as heat and work can vary depending on the path (how you get from an initial to a final state). In contrast a defining aspect of a state function is that it is independent of the path.

Entropy is a state function, as a corollary therefore a path-independent property. The experimental determination of entropy involves measuring the heat transferred as a function of temperature during a reversible process and computing $\int \frac{dq}{T}$. That is another defining property of the entropy. It is not trivial to wrap your head around why it should be so, but entropy can be thought of as helping quantify a limiting or ideal property, in particular the maximum work that might be obtained from a process, or the least amount of work required to bring about a non-spontaneous change. It defines processes in which there are no losses (losses being consistent with irreversibility).

As an example, at constant T and p the Gibbs free energy change (which is related to the limiting work) is related to the entropy as follows:

$$-\frac{\Delta G}{T}=\Delta S_{system}+\Delta S_{surrounding}$$