Exergy

Exergy (also called availability) is the maximum useful work obtainable from a system as it is brought reversibly to thermodynamic equilibrium with a defined reference environment (dead state) specified by temperature T0 and pressure p0. Exergy is not conserved: irreversibilities generate entropy and destroy exergy. Exergy quantifies useful work potential and separates loss into unavoidable heat transfer to the environment and avoidable exergy destruction. There are different contributions to exergy: physical (due to temperature and pressure differences), kinetic and potential, and chemical (due to composition differences relative to the environment). For open systems, the flow (or stream) exergy uses enthalpy and entropy (h and s); for closed systems non-flow exergy uses internal energy and entropy (u and s).

Governing FormulaKey relations and formulas (SI units): - Definition (non-flow exergy per unit mass): e = (u - u0) - T0 (s - s0) + (ke + pe) - Flow (specific) exergy per unit mass (including kinetic and potential): e_flow = (h - h0) - T0 (s - s0) + ke + pe - For an ideal gas (constant cp, R): e_flow = cp (T - T0) - T0 cp ln(T/T0) + R T0 ln(p/p0) + ke + pe - Gouy–Stodola theorem (rate form): E_dot_destruction = T0 * S_dot_generation - Maximum useful work from heat transfer Q at temperature T to environment T0 (reversible Carnot limit): W_max = Q (1 - T0/T) - Exergy balance, general rate form for control volume (steady or transient): Exergy_in - Exergy_out = W_dot_net + E_dot_destruction + d(Exergy)/dt (for steady-state d(Exergy)/dt = 0) - Exergetic (second-law) efficiency: eta_ex = (useful exergy output) / (exergy supplied as input) Notes/assumptions: T0 is absolute temperature of the environment; h0, u0 and s0 are properties at the dead state (T0,p0).

Knowledge Check

10 Questions

1.Which statement best defines the thermodynamic exergy of a system with respect to a specified environment (dead state) at temperature T0 and pressure p0?

2.Gouy–Stodola theorem relates exergy destruction rate E_dot_d to entropy generation rate S_dot_gen. Which is the correct relation (T0 is the environment temperature)?

3.Which expression correctly gives the specific flow exergy (per unit mass) of a fluid stream excluding kinetic and potential terms (h and s are at stream conditions, subscript 0 indicates dead state)?

4.A closed system receives Q = 100 kJ of heat reversibly at a uniform temperature T = 500 K. The environment (dead state) is at T0 = 300 K. What is the maximum useful work that could be extracted from this heat transfer alone (assume reversible transfer)?

5.A process in an engineered device generates irreversible entropy at a rate S_dot_gen = 0.200 kJ/K. The environment temperature is T0 = 298 K. What is the exergy destroyed (in kJ) associated with that entropy generation (assume steady process and consider a single event with the given total S_gen)?

6.Which statement correctly lists the full components included in the specific flow exergy of a real fluid stream (per unit mass)?

7.Air (ideal gas, cp = 1.005 kJ/kg·K, R = 0.287 kJ/kg·K) is at T = 600 K and p = 500 kPa. The environment is at T0 = 300 K and p0 = 100 kPa. Neglect kinetic and potential energies. What is the specific flow exergy e (kJ/kg) of this air? Use e = cp (T - T0) - T0 cp ln(T/T0) + R T0 ln(p/p0).

8.Which formula gives the exergetic (second-law) efficiency of a device in general form?

9.Which factor most directly determines the chemical exergy of a fuel relative to a reference environment?

10.A steady turbine processes an air mass flow of m_dot = 2.00 kg/s. The specific flow exergy of the inlet stream is 231.12 kJ/kg and of the outlet stream is 50.00 kJ/kg. The turbine produces shaft power W_dot = 300 kW. Neglect heat transfer to environment and ke/pe changes. What is the exergetic (second-law) efficiency of the turbine (useful exergy output divided by exergy decrease of the fluid)?