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[tex]A=U-U_o+P_o(v-v_o)-T_o(S-S_o)[/tex] being: (1)

[tex]U[/tex] Internal energy

[tex]P[/tex] Pressure

[tex]v[/tex] Specific volume ([tex] 1/\rho[/tex])

[tex]T[/tex] Temperature

[tex]S[/tex] Entropy

Subindex "o" refers to the Dead State: the thermodynamic state of the atmosphere.

Thus, the maximum work available from a thermodynamic closed system submerged into an atmosphere [tex]P_o,T_o[/tex] is:

[tex]W_{max}=A[/tex]

In general, the nominal work extracted would be less, due to irreversibilities:

[tex] W=A-T_o\Delta S_{universe}[/tex]

Let me do the next: take differential in expression (1):

[tex] dA=dU+P_odV-T_odS_{sys}[/tex] (2)

in addition to 1st principle and Entropy definition:

[tex] \delta Q=dU+\delta W=TdS_{sys}-TdS_{universe}[/tex] (3)

substituting (3) in (2), and defining the useful work as the net work substracting the work done by the atmosphere [tex]\delta W_{useful}=\delta W-P_odV[/tex], we have:

**[tex] dA=-dW_{useful}+\delta Q\Big(1-\frac{T_o}{T}\Big)-T_odS_{universe}[/tex]**

Let's take a look at this last expression. We see effects of extracting work, global irreversibilities and extracting heat enhances a loose of Availabilty and so a loose of mechanical energy available for doing work.

__The question__: Imagine the system is absorbing heat due to some process of burning such it happens in an internal combustion engine at combustion stage, or merely there is an inflow of heat due to some thermal contact.

__Only some percentage of Heat would be available for doing work, in particular this fraction would be [tex] \Big(1-T_o/T\Big)[/tex]. On the contrary the part of heat unavailable for doing work is called "Anergy" and would be [tex]QT_o/T[/tex]. The question is:__

**Assume there is no global irreversibility**.**Where does this Heat unavailable for doing work go?**

**What is its mission?**

Thanks for clarifying this concept, I really don't know which is the physical mission of this unavailable heat, assuming there is no irreversibility, as we have seen this term can be dropped without affecting the answer of my question.