Violation of the second law of thermodynamics?

[Azorspace]

Homework Statement

This is a basic conceptual question that i encountered when i was reading the section on Entropy on the book by K. Huang on statistical mechanics, it goes like this. In a reversible isothermal expansion of an ideal gas, i know that the change in internal energy is zero, which leaves, by the use of the first law an expression that says that the heat absorbed by the system is equal to the work done, which is a violation of the second law, because it's saying that the system converts all the heat into work, so why does this is a valid transformation?

The Attempt at a Solution

I think that we need to add another term that involves dissipation.

 

[collinsmark]

It's been a really long time since I've taken thermodynamics, so bear with me. (If anybody else wants to jump in, by all means do so). But since nobody has responded yet to this post yet, I'll give it a shot on a few hints.

The second law of thermodynamics states for a closed system (overall),

ΔS_total ≥ 0

But keep in mind,

ΔS_total = ΔS_{internal_system} + ΔS_surroundings

Keeping all that in mind, note that the relationship in the second law is a "≥" sign, and not a ">" sign. There are situations where total entropy can remain unchanged (that's where the "equal to" part of the "greater than or equal to" fits in).

[Edit: Well, "ideal, theoretical situations" I should have perhaps said.]