[Burningkrome]

This is either a freshman question, or a huge can of worms.

ΔS_Internal + ΔS_External ≥ 0

When could this ever be more than zero?

As I understand it (regardless of whether using the statistical or thermodynamic definitions of entropy), this can't happen because ΔS_External DEFINES ΔS_Internal and vice-versa.

I.e.
Q = the change in thermal energy PUT INTO the system from surrounding.

ΔS_Internal = Q/T
and
ΔS_External = the heat put into the system by surrounding, or -Q/T

Q is the same energy, by definition. Thus ΔS is equal and opposite, by definition. Or not?

[Schrödinger]

ΔS_Internal = Q/T

What you need to understand here is that it's not just Q. ΔS_Internal = Q_rev/T.
Only when the process is carried out reversibly can you say that ΔS_Internal = Q/T. This is when the equality with 0 holds : ΔS_Internal + ΔS_External = 0

In case the process is carried out irreversibly, then ΔS_Internal + ΔS_External > 0 (strictly positive, not equal to 0). In this case, you cannot say ΔS_Internal = Q/T, because ΔS_Internal ≠ Q_irrev/T

[curiouscat]

In case the process is carried out irreversibly, then ΔS_Internal + ΔS_External > 0 (strictly positive, not equal to 0). In this case, you cannot say ΔS_Internal = Q/T, because ΔS_Internal ≠ Q_irrev/T

I agree but to further the riddle: Aren't all processes reversible on a microscopic scale? If so, is the equality always valid at that scale?

[Burningkrome]

So, I may be misunderstanding a number of terms. My understanding of the functional  definition of entropy is heat lost without work. Example; an exothermic reaction dissipating heat out of the system and increasing ΔS_External.

I understand the statistical definition of entropy as (loosely) being the “probability of the system being in one of the sum of all the possible positions of the micromolecular structure times -bK”. So a spinning coin = a ΔS_system of 2*-bK (clockwise and counterclockwise) then two spinning coins = a ΔS_system of 4*-bK, 3 coins 6*-bK, ETC.

So, the definitions I have are…
Q = Heat ADDED to system from external.
So, Q_system = -Q_External and Q = ΔH and –Q = -ΔH
From this ΔS_system = Q/T and since Q = -Q then ΔS_External = -Q/T

I’m guessing some or all of these definitions are wrong. Can you help me re-define them?