Gestão de Sistemas Energéticos 2016/2017 Exergy Analysis Prof. Tânia Sousa taniasousa@tecnico.ulisboa.pt

Evaluating Enthalpy for Reactive Systems The specific enthalpy of a compound (in this datum) at a state where temperature is T and pressure is p is determined from What is the value of in the datum used to assign the enthalpies of formation? h is associated with the change in state from the standard state to the state where temperature is T and the pressure is p (obtained from any table).  

Heating Values of Hydrocarbon Fuels

Heating Values of Hydrocarbon Fuels The heating value of a fuel is the difference between the enthalpy of the reactants and the enthalpy of the products when the fuel burns completely with air, reactants and products being at the same temperature T and pressure p.

Heating Values of Hydrocarbon Fuels The higher heating value (HHV) is obtained when all the water formed by combustion is a liquid. The lower heating value (LHV) is obtained when all the water formed by combustion is a vapor.

Heating Values of Hydrocarbon Fuels TABLE A-25

Example C8H18 + 12.5(O2 + 3.76N2) → 8CO2 + 9H2O(g) + 47N2 Evaluate the lower heating value of liquid octane at 25oC, 1 atm, in kJ per kg of octane, and compare with the value provided in Table A-25. C8H18 + 12.5(O2 + 3.76N2) → 8CO2 + 9H2O(g) + 47N2

Example Evaluate the lower heating value of liquid octane at 25oC, 1 atm, in kJ per kg of octane, and compare with the value provided in Table A-25. This value agrees with the value (44,430 kJ/kg for C8H18) from Table A-25, as expected. LHV = 5,074,630 kJ/kmol C8H18 LHV = 44,429 kJ/kg C8H18

Evaluating Entropy for Reactive Systems Absolute Entropy For reacting systems, a common datum must be used to assign entropy values to participating substances: the entropy of a pure crystalline substance is 0 at T=0K (the third law of thermodynamics) Values of entropy determined relative to this datum are called absolute entropy values. Are the entropies given in A2 absolute entropies?

Evaluating Entropy for Reactive Systems Absolute Entropy For reacting systems, a common datum must be used to assign entropy values to participating substances: the entropy of a pure crystalline substance is 0 at T=0K (the third law of thermodynamics) Values of entropy determined relative to this datum are called absolute entropy values. Steam tables and Tables A-7 through A-18 do not provide absolute entropy values.

Absolute Entropy TABLE A-25

Absolute Entropy TABLE A-23

Absolute Entropy The specific absolute entropy of a compound at a state where temperature is T and pressure is P is determined from For the ideal gases in Table A-23, the absolute entropy at a state where temperature is T and pressure is p is given by For the component i of an ideal gas mixture º ref ref Partial pressure

Example C8H18 + 12.5(O2 + 3.76N2) → 8CO2 + 9H2O(g) + 47N2 Compute entropy production for complete combustion with a) theoretical amount of air and b) 400% theoretical air. C8H18 + 12.5(O2 + 3.76N2) → 8CO2 + 9H2O(g) + 47N2

Reacting Systems: combustion Simplifying assumptions: air and exhaust gases are considered a mixture of ideal gases

Reacting Systems: combustion Simplifying assumptions: air and exhaust gases are considered a mixture of ideal gases

Evaluating Gibbs Function for Reacting Systems The specific Gibbs function g is given by Gibbs function is a property because it is defined in terms of other properties.

Evaluating Gibbs Function for Reacting Systems The specific Gibbs function of a compound (in this datum) at a state where temperature is T and pressure is p is determined from In an ideal gas mixture, the specific Gibbs function is evaluated at Pi

Evaluating Gibbs Function for Reacting Systems TABLE A25

Evaluating Gibbs Function for Reacting Systems A Gibbs function datum for the study of reacting systems is established by: Assigning a value of zero to the Gibbs function of C, H2, N2, O2, and other stable elements at the standard reference state defined by Tref = 298.15 K (25oC) and pref = 1atm. The Gibbs function of a compound at the standard state equals its Gibbs function of formation is the change in the Gibbs function for the reaction in which the compound is formed from its elements, the compound and elements all being at the standard state.

Exergy Exergy is … Thermomechanical exergy: if temperature and/or pressure of a system differ from that of the environment; Chemical exergy – if there is a composition difference between the system and environment;

Evaluating Chemical Exergy The exergy reference environment (the Earth and its atmosphere) Environmental temperature T0 and pressure p0. Set of reference substances with concentrations closely corresponding to the chemical makeup of the natural environment. Reference substances may include Gaseous components of the atmosphere: N2, O2, CO2, H2O(g), and other gases. Solid substances from the Earth’s crust. Substances from the oceans.

Conceptualizing Chemical Exergy CaHbOc enters the control volume at T0, p0. O2 and CO2, H2O(g) enter and exit the control volume at T0 and their respective partial pressures. The ideal gas model applies to O2, CO2, and H2O(g).

Conceptualizing Chemical Exergy Negligible kinetic and potential energy effects Heat transfer between the control volume and environment occurs only at temperature T0 Steady state The chemical exergy per mole of CaHbOc, ech, is the maximum theoretical value of Wcv/nF

Conceptualizing Chemical Exergy The logarithmic term typically contributes only a few percent to the chemical exergy magnitude

Example Compute the exergy of methane, CH4, when T0 = 298.15 K (25oC), p0 = 1 atm.

Example Compute the exergy of methane, CH4, when T0 = 298.15 K (25oC), p0 = 1 atm.

Example Compute the exergy of methane, CH4, when T0 = 298.15 K (25oC), p0 = 1 atm.

Example Compute the exergy of methane, CH4, when T0 = 298.15 K (25oC), p0 = 1 atm.

Example What is the pure CO2 exergy, when T0 = 298.15 K (25oC), p0 = 1 atm?

Example Compute the exergy of pure CO2, when T0 = 298.15 K (25oC), p0 = 1 atm.

Example Compute the exergy of CO2, when T0 = 298.15 K (25oC), p0 = 1 atm. Applies also to other gases in the environment

Example What about the exergy of H2O, when T0 = 298.15 K (25oC), p0 = 1 atm?

Example What about the exergy of H2O, when T0 = 298.15 K (25oC), p0 = 1 atm?