The Decrease of Exergy Principle and Exergy Destruction

By David Hall

The Decrease of Exergy Principle

The decrease of exergy principle is the counterpart of the increase of exergy principle. By definition, no heat, work, or mass can cross the boundaries of an isolated system, meaning there is no energy and entropy transfer. As a result, the energy and entropy balances for an isolated system can be expressed as -

             Energy Balance:     Ein - Eout = ΔEsystem → 0 = E2 - E1

                                                               0↗      0↗

             Entropy balance:    Sin - Sout + Sgen = ΔSsystem → Sgen = S2 - S1

                                                               0↗      0↗

Multiplying the second relation by T0 and subtracting it from the first gives -

             -T0Sgen = E2 - E1 - T0(S2 - S1)

Additionally, we know that -

              X2 - X1 = (E2 - E1) + P0(V2 - V1) - T0(S2 - S1)

                                                   0↗

              = (E2 - E1) - T0(S2 - S1)

Since V2 = V1 for any isolated system. Combining the previous 2 equations gives -

              -T0Sgen = X2 - X1 ≤ 0

T0 is the thermodynamic temperature of tenvironment, and is therefore a positive quantity. Sgen ≤ 0, meaning T0Sgen ≤ 0. From this it can be seen that -

              ΔXisolated = (X2 - X1)isolated ≤ 0

This equation that during a process in an isolated system, exergy always decreases, unless the process is perfectly reversible in which case it remains constant. No process can ever be truly reversible however, meaning for an isolated system exergy is always destroyed during a process.

Exergy Destruction

All irreversible processes result in entropy being generated. Using the equation below, it can be seen that the exergy destroyed is proportional to the entropy generated -

        Xdestroyed = T0Sgen ≥ 0

Any process can be thought of as taking place in an isolated system, and therefore this equation can be applied to any process. Exergy destroyed represents the lost work potential and can be known as irreversibility or lost work. If the exergy destroyed takes a positive value, the process is feasible but irreversible, if it is 0, the process is perfectly reversible and if it is negative, meaning exergy is generated during the process, then the process is not feasible or reversible. No process is truly reversible, and therefore any actual process has a positive value for exergy destroyed, which means that the exergy in the universe is constantly decreasing in the same way the entropy is increasing.