What is non PV work? How is it related to Gibbs energy?

Recently, I was trying to understand more about Gibbs free energy and got stuck at this point. Some books write that if $\Delta G=0$, then the reaction is reversible while some other sources say that a reaction is reversible when $\Delta G$ = Non-$PV$ work.
I am not able clarify things here and am unable to understand the core concept of non $PV$ work.




At **constant temperature and pressure**, the maximum non expansion work is given by the change in the Gibbs Free Energy. 


$$dW\_{\text{max}}= dG$$ 


**Proof:**


At constant temperature and pressure, 


* from the definition of enthalpy: $H= U+pV$
* first law of thermodynamics: $dU = dq+dw$


$\implies dH = dq+ dw + d(pV)$


Now, 


$dG = dH - TdS -SdT \\\implies dG = dq + dw + d(pV)- TdS - SdT$


For isothermal process $dT =0$


$\implies dG = dq+dw+ d(pV)+ -TdS$


When the change is reversible, 


$dq = dq\_{\text{rev}}= TdS$ and $dw= dw\_{\text{rev}}$


$\implies dG = dw\_{\text{rev}}+d(pV)$


The work consists of expansion work, which for a reversible change is given by
−pdV, and possibly some other kind of work (for instance, the electrical work of
pushing electrons through a circuit or of raising a column of liquid); let's denote it by $dw\_{\text{add},\text{rev}}$


$\implies dG= dw\_{\text{add}, \text{rev}}+ Vdp$


For isobaric process, $dp =0$


$\implies dG = dw\_{\text{add}, \text{rev}}$ 


You must be aware the the **maximum work is obtained when the process is reversible**, if not you may refer to [this answer](https://physics.stackexchange.com/questions/14012/why-is-the-maximum-work-achieved-in-reversible-processes). 


$\implies dG = dw\_{\text{add}, \text{max}}$



> 
> Some books write that if $\Delta G=0$, then the reaction is reversible while some other sources say that a reaction is reversible when $\Delta G$ = Non-$PV$ work.
> 
> 
> 


$\Delta S\_{\text{total}}= \dfrac{-\Delta G\_{\text{system}}}{T}$


Thus, for a reversible process $\Delta G\_{\text{sys}}= 0$


And I have also proved to you above that $\Delta G\_{\text{sys}}=$ maximum non expansion (non PV) work. 



> 
> I am not able clarify things here and am unable to understand the core concept of non $PV$ work.
> 
> 
> 


PV work is only the work done during the *change in volume*. There can be different types of works that a system can do during a process, for instance: [electrical work](https://en.wikipedia.org/wiki/Work_(electrical)), work against gravity, work against friction, magnetic work, shaft work, etc. This is the concept of non expansion or non PV work. 


**Source:** 


* Physical Chemistry by Atkins (8th ed. )
* [Wikipedia article on work in thermodynamics](https://en.wikipedia.org/wiki/Work_(thermodynamics))


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