You can read this http://wvuscholar.wvu.edu:8881//exlibris/dtl/d3_1/apache_media/L2V4bGlicmlzL2R0bC9kM18xL2FwYWNoZV9tZWRpYS8yMDk0Nw==.pdf
It basically says you add the thermal conductivities weighted by volume ratio. But that may only be for mixtures that meet certain blending criteria.
You are right that a seemingly complex diagram or sequence can be described by a simple iteration and so therefore contains little information. But there are many seemingly complex sequences or expressions that have a simple basis (for example an lfsr based random number generator). Given to...
Not sure I understand the PE part, but, roughly speaking, for any material the attractive forces between molecules is defined and "constant" so the amount of vibration it takes to break it loose is fixed and consistent. Are you asking why the amount of vibration needed to break them loose...
Right.
Think about a rock and a block of ice and the effect of a phase change. The ability to transfer energy between them can be understood easily it terms of temperature, but what other units allow that fundamental understanding and is consistent through phase change?.
When the kinetic energy is enough to overcome the attractive force between molecules it becomes a gas. But you probably already knew that. The details are described nicely in the page.
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/phase.html
Especially this section:
Some energy details...