Recall in physical chemsitry and 1st year chemsitry, we have came across Gibss free energy and some examples of endothermic process, e.g. solvation of NH4Cl

Such process works despite having a positive enthalpy change is because it is offset by the increase in entropy as the ions get solvated

Now recall the conceptual ideas of entropy in chemistry

1. Molecules that are quite floppy (thus can wiggle more) have higher entropy

2. Entropy measures the extent of spreading of energy among the molecule's various modes

Now recall second law

entropy of an isolated system increases over time until it maximize at thermodynamic equlibrium

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Now my question is, if all that is needed for second law to be happy is to increase entropy, and entropy (for most purpose in chemistry) is a measure of energy spread

If we have a molecule which is incredibly porous and incredibly floppy (let's call this A), can we do the following?

1. A has temperature T K (thus has energy U1)

2. A piece of iron block has temperature

**T+1**K (and has energy U2)

3. Now stick the iron to A. Because A is incredibly floppy, the entire system A+Iron is many orders of magnitude more floppy than the iron

4. Heat (Q) will flow from hot to cold as expected, in order to increase the entropy of A+Iron by attaining equlibrium

5. Meanwhile, we attached a battery (assume 100% efficient and no loss over time) in between to convert some of the heat into electricity and stored into it. Thus we basically make a heat engine with work (W) extracted from a reservoir

a. Can Q be made arbitrarily small (NOT ZERO, as this is impossible), so it is in the order of 10^-30, due to the incredibly floppy nature of A+Iron will allow a small amount of energy to be distributed over (maybe) a gazillon of thermal modes, thus able to meet the entropy requirement of the 2nd law, or is this impossible because Carnot's Theorem also have taken account of this and Q can never met the requirement if it is too small, even if the final state has a lot more possible microstates (chem: ways to wiggle)?

b. If a is no, how to modify the calculations in Carnot theorem in order to introduce the factor of microstates of A (which can be set to any value to analyse different A, let's call this factor B) and show that there is a limit to how small Q can get even if B tends to infinity?

c. do the rate of heat transfer depends on the total number of microstates in the final state of the system (that is will the transfer be more rapid if the final state of the system has more microstates? (Analogy, like how gas expanding to a very large container is quicker than the small one, given same initial pressures each for both containers))

I am kinda rusty because the stuff is a year away, thus apologies if I missed out some obvious theorems that I could have used and help and reminder would be appreciated if that's the case

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