Work done for an adiabatic process

[A_B]

Hi,

In deriving the equation for adiabats : $V^{\gamma}P = C$. It is assumed that the work done during the process is $W = -P \Delta V$.

But calculating the work done from $V^{\gamma}P = C$ we obtain:

$$W = \frac{C}{1-\gamma}\left[ V^{1-\gamma}_{f} - V^{1-\gamma}_{i} \right]$$.

Also, i believe to have heard that the assumption used for the derivation ($W = -P \Delta V$) is due to the assumption that the process is quasi-static, how does that work exactly?

Thanks

 

[A_B]

whoops, never mind, the derivation uses $W = -P dV$ for an infinitesimal change, that makes sense, but I'd still like some more info on what a quasi-static process means and where in the derivation it's used.