All the basic texts say $dQ = T dS$. Some say it is possible to define absolute entropy. That source gives an equation integrating C dT which should reduce to $Q=ST$, if $S(0) = 0$ and $Q$ is defined as all the heat that can possibly be extracted from the object. But it seems like sources overwhelmingly avoid writing $Q=ST$. If I could use that equation it should be simple to visualize the nature of entropy... (see below)
This would also seem to make entropy the number of different variables that have been able to take up thermal energy. But when taking actual entropy values, for example, 131 J/mol K for H2, 192 J/(mol K) for N2, and 193 J/(mol K) for NH3 at STP - the values are many times larger than the gas constant. Is there a way to conceptualize entropy to break down these numbers into 46 different degrees of freedom, or is this comparison intrinsically flawed? Why?
EDIT: in light on ongoing discussion, I'd like to quote a very basic exercise from LibreTexts that made me start thinking about this issue:
Calculate entropy change when 36.0 g of ice melts at 273 K and 1 atm. [enthalpy of fusion 6.01 kJ/mol].
Their solution is $\Delta S$ = (6.01 kJ mol-1)/272 K * (36 g)/(18 g mol-1) = 1.22 kJ / K
This illustrates we can have more than one entropy value for the same temperature, and also something of a surprising result, namely that the higher the melting point of the substance, the less melting it affects the entropy. Of course, this is countered by likely requiring more energy to do the actual melting as reflected in the enthalpy value, but still, it made me wonder what this denominator means. The interpretation I want to give is that there is a pool of heat energy which is larger at higher temperature, and the total entropy has been increased in proportion to the expanded capacity to store heat at the same temperature. But this would imply thinking of a relationship between these total quantities.