Exergy

1. Exergy Phase 2

2. Exergy destruction • Caused by irreversibilities such as: • Friction, mixing, chemical reactions, heat transfer through a finite temperature difference, unrestrained expansion, non-quasi-equilibrium compression or expansion; anything that cause entropy generation Anything that generates entropy, destroys exergy

3. Exergy destruction • Exergy destroyed is proportional to entropy generated • Xdestroyed = T0Sgen ≥ 0 • Exergy destroyed represents the lost work potential, also called irreversibility or lost work

4. Exergy destruction • > 0 irreversible system • Xdestroyed = 0 reversible system • < 0 impossible system • Apply to all systems since we can make the boundary of the system large enough to enclose surroundings in system

5. Exergy Balance • Exergy balance: any system Xin –Xout –Xdestroyed = ΔXsystem (kJ) • Exergy balance: any system, unit mass • xin –xout –xdestroyed = Δxsystem (kJ/kg) • Exergy balance: rate form

6. Exergy Balance • Closed systems:

9. Exergy destruction • In the rate form:

10. Exergy destruction • For unit-mass (xin–xout) – xdestroyed = Δxsystem (kJ/kg) • For reversible process xdestroyed term goes to 0 • Xdestroyed = T0Sgen

11. Exergy destruction • The exergy change of the system, if the environment is known, can be determined from the end states, (ΔXsystem= X2–X1) however, the exergy transfer for the heat, work and mass transfer must be determined with knowledge of the states and process.

12. Exergy destruction • For closed system (no mass flow) • Xheat–Xwork- Xdestroyed = ΔXsystem • ∑(1-T0/Tk)Qk – [W-P0 (V2–V1)] –T0Sgen = X2- X1 where Qk is the heat transferred through the boundary at temperature Tk at location k. • Also a rate form

13. Exergy destruction • Wrev can be found by setting W = Wrev and Xdestroyed = T0Sgen = 0 • Equation represents the exergy destroyed within the system boundaries only, so if 0 may be internally reversible only • Expand system boundaries to include surroundings to find irreversibilities in surroundings

14. Exergy destruction • For a reversible process, entropy generation and exergy destruction are zero, exergy balance becomes similar to energy balance • Energy change of a system for any process equals the energy transfer. For exergy the change equals the transfer for only reversible processes

15. Exergy destruction • The quantity of energy remains constant (1st law) for actual processes but the quality of the energy (2nd law) decreases. • Accompanied by an increase in entropy and decrease in exergy

22. Exergy Balance • Control volumes, add mass flow • Xheat–Xwork+(Xmass in –Xmass out ) - Xdestroyed = ΔXCV • ∑(1-T0/Tk)Qk – [W-P0 (V2–V1)]+∑miψi –∑meψe-T0Sgen = (X2- X1)CV • Also a rate form

23. Exergy Balance • The rate equation is the rate of exergy change within the control volume during a process is equal to the rate of net exergy transfer through the control volume boundary by heat, work, and mass flow minus the rate of exergy destruction within the boundaries of the control volume.

24. Exergy Balance • When the initial and final states of the control volume are known then • X2–X1 =m2Φ2- m1Φ1

25. Exergy Balance • Steady-flow systems (Fig 7-43) • Amount of exergy entering must equal amount leaving and destroyed.

26. Exergy Balance: steady flow • Control volumes used the most are turbines, nozzles, diffusers, heat exchangers, pipes, compressors, and ducts • Operate steady state, no change in mass, energy, entropy, exergy, volume • Amount of exergy entering must equal amount leaving and destroyed