# What does it mean to define entropy as a measure of a systems internal energy per unit temperature which is unavailable to do work?

Entropy was defined in one of my findings as "the measure of the internal energy of a system per unit temperature which is unavailable to do work". Can someone help me understand this definition better cause I have always defined entropy as the degree of disorder in a system.

The answer to this question goes back to the Gibbs equations according to which $$\mathrm{d}U=T\,\mathrm{d}S-p\,\mathrm{d}V$$ and for a reversible process $$đq = T\,\mathrm{d}S$$ So, if you have a change in internal energy $\mathrm{d}U$ and it does work $p\,\mathrm{d}V$ then it has also absorbed $T\,\mathrm{d}S$. The verbiage you are quoting is very awkward and is not very useful, nevertheless for your future studies you will be better off if you will never think of entropy as "disorder" in any sense. Entropy is not disorder and such concept will never help you solve any real problem. Also, never think of a body containing "heat"; a body has energy depending on its state but independent of external constraints; and it has entropy that depends both on its state and its external constraints. For example, an ideal gas after it has expanded into a larger volume has the same energy as before it has done no work and absorbed no heat but its entropy is larger than it was in a smaller available volume. The entropy is the same in all possible molecular configuration consistent with the volume, so it is the same whether the molecules occupy uniformly the available volume or because of a large fluctuation spontaneously collapse into a smaller volume form the larger one. So it is the constraint (the available) volume that determines the entropy not how the molecules are distributed in it in any given instant of time. No disorder.
• I was always in dilemma with the thermal energy associated with entropy as being unavailable to do work..... I mean then how could Carnot engine work? Thermal energy is absorbed in the engine from the hot reservoir it's associated with entropy change. Is this thermal energy unavailable to do work? No; A part of this heat/thermal energy gained due to the entropy change is used for work. So, I couldn't believe that phrase unavailable to do work.