Why there isn't a work term in entropy balance equation?

[alpyurtsever]

1. The problem statement, all variables and given/known data

Hi, I need your help in my homework. My Instructor asked that question? Why there is not a work term in entropy balance equation?


2. Relevant equations

http://upload.wikimedia.org/math/a/b/b/abb639ee87e7f36fd877e3e212a87f41.png

3. The attempt at a solution

I have researched about it and I found that,

entropy has not an exact physical meaning, however it is associated with disorder or randomness. In another point of view, entropy defines the energy which is unable to do work.
however I am not sure that these definitions are enough.

On the other hand, I think entropy is a mathematical derivation, which is done by a purpose of having a balance equation which does not involve a work term.
They have originated it from the one directional flow of heat (from high temperature to low). Is it true?

Thanks for your help

[Mapes]

One way of looking at it is that doing work on a system changes the levels of its energy states, while transferring heat to a system changes the population of states. Entropy is quantified by the number of possible microstates (e.g., atomic arrangements) that are compatible with our macrostate observation (of pressure, for example). Since changing energy levels en masse doesn't affect the number of compatible microstates, doing (reversible) work on a system doesn't transfer any entropy, and the entropy rate in the equation above doesn't depend on work.