Re: Relation among specific heat, thermal conductivity, and time?

I'll take a shot at answering all your questions except #4 -- there are 
professional career counselors for that.

1) The specific heat is only one factor that determines how fast something 
will heat up or cool down.  You have to think of this in terms of energy 
being transferred.  For the same amount of energy, you will get 5 times as 
much temperature rise out of a gram of granite as a gram of water.  But 
you also have to transfer the energy, and that is where the thermal 
conductivity is important (among other things).  So a block of iron will 
heat up much faster if exposed to a high temperature than will the equal 
weight of water or granite -- that has very little to do with the specific 
heat and everything to do with the thermal conductivity.
Transparency to light *usually* makes no difference.  The exception would 
be if you were transferring heat by radiation, which is only important at 
pretty high temperatures.
As I said before, there are a lot of ways to transfer heat, so there are 
no general answers to questions like those you are asking unless the 
specific conditions are specified.

2) There are a number of materials with a specific heat like water or 
higher (hydrogen, helium, lithium metal, LiH, ammonia, etc.).  But nothing 
I can think of that one would normally build a wall out of.  However, if 
the purpose of the wall is to keep heat from getting from one side to the 
other, it is the thermal conductivity (and, of course, the thickness of 
the wall) that matters.  The specific heat will only make a difference if 
the amount of energy it takes to heat up the wall in some transient 
situation is substantial compared to the total amount of energy being 
transferred across.  The insulation in your house is chosen for its low 
thermal conductivity, not its specific heat.

3) I find a specific heat (again, in Perry's Chemical Engineers Handbook) 
of 0.32 for cellulose.  I'd guess paper would be in that ballpark.