Clausius Clapeyron equation While reading about the Clausius Clapeyron equation from the Feynman lectures on Physics, I couldn't understand a few things from its derivation:
Although the argument was pretty clear, when the system consists both gas(vapour) and liquid why would it have constant pressure on heating and increasing volume?? 
Second and more fundamental, how can we assign a single pressure value to this composite system in spite of it having two states of matter; wouldnt the pressure in the gas part (on top part of container) be different from that at the bottom or side in the liquid part? On top of this how can this be the vapour pressure (which I think is the pressure of the vapours on the surface of liquid)? 
 A: The system has constant pressure by definition. Even in a system with changing pressure, though, for some small time, dt, there would be constant pressure. In that moment, and with those conditions, the relationship holds. Adjust the pressure slightly, and a new, similar relationship is set up.
The second question is related to this being a thought experiment (an ideal situation). If gravity isn't a factor, the pressure remains constant throughout the container. The International Space Station may be the best environment for testing this out, and I suspect someone may get around to trying it, if they haven't already.
A: Concerning the second question:
Consider the Volume $V$, filled with the two phases of the substance. Assume that the pressure in the liquid is $p_\mathrm l$ and the pressure in the vapor is $p_\mathrm v$. In the abstinence of an external pressure $p_\text{ext}$ the assumption $p_\mathrm l\neq p_\mathrm v$ would imply that the vapor/liquid would expand and the liquid/vapor would be compressed. Therefore in equilibrium (no ongoing expansion of any phase allowed) the condition
$$
p_\mathrm v=p_\mathrm l:=p
$$
has to be met, so that the pressures at the interface of the two phases compensate each other.
Further reading: This equality will not hold true if for example there is a external pressure due to surface tension or inertial pressure caused by a secondary gas in the volume $V$. See this question: Derivation of the Poynting and Kelvin equation (Effect of external pressure on vapor pressure)
