# Why is dp/dv zero for a real gas in critical conditions?

I have read this fact in various websites but cannot understand the reason. What is an intuitive explanation of this?

This is merely a shard of a fact which does not make much sense in and by itself. After all, in systems with gas/liquid equilibrium there is nothing really special about $\left(\dfrac{\partial\mathfrak p}{\partial V}\right)_T=0$. On the contrary, this is pretty typical. See all those points where the blue lines (isotherms) are horizontal? They make up a whole huge area on the diagram.
Well, then there must be a temperature where this behavior changes, and that's what we call the critical temperature. Sure enough, it produces a very special isotherm: there is only one point on it where $\left(\dfrac{\partial\mathfrak p}{\partial V}\right)_T=0$. (That's what we call the critical point, BTW.) Moreover, since it is an inflection point, it also has $\left(\dfrac{\partial^2\mathfrak p}{\partial V^2}\right)_T=0$. Now that's the fact one should remember about the critical point.