Which is coldest?

You heat a disc with a hole in it. Will the diameter of the hole get larger,
smaller, or stay the same?

Suppose we have two jars of gas: one of helium and one of neon. If
both jars have the same volume, and the two gases are at the same pressure and
temperature, which jar contains the greatest number of gas molecules? (Both gases obey the ideal gas law.
The mass of a neon molecule is greater than the mass of a helium
molecule.)

Ralph is confused about the reading assignment (as usual...). The book calls
two different equations "the ideal gas law". In equation 10.8 (8th edition), the
equation is "PV = nRT". But in equation 10.11 (8th edition), the equation is "PV
= Nk_{B}T". Why are they both called the ideal gas law, when only the
first equation looks like what he learned in chemistry? Why is one "n" lower
case and the other one upper case? What can you tell Ralph to help him
understand these two equations?