Thermodynamics

If a gas mixture is at a relatively high pressure or low temperature, thedeviation from the ideal-gas behavior should be accounted for by incorporatingmore accurate equations of state or the generalized entropy charts.15–7 SECOND-LAW ANALYSISOF REACTING SYSTEMSOnce the total entropy change or the entropy generation is evaluated, theexergy destroyed X destroyed associated with a chemical reaction can be determinedfrom(15–23)where T 0 is the thermodynamic temperature of the surroundings.When analyzing reacting systems, we are more concerned with thechanges in the exergy of reacting systems than with the values of exergy atvarious states (Fig. 15–30). Recall from Chap. 8 that the reversible workW rev represents the maximum work that can be done during a process. In theabsence of any changes in kinetic and potential energies, the reversible workrelation for a steady-flow combustion process that involves heat transferwith only the surroundings at T 0 can be obtained by replacing the enthalpyterms by h – ° f h – h – °, yielding(15–24)An interesting situation arises when both the reactants and the products areat the temperature of the surroundings T 0 . In that case, h – T 0 s – (h – T 0 s – ) T0 g – 0 , which is, by definition, the Gibbs function of a unit mole of a substanceat temperature T 0 . The W rev relation in this case can be written asorX destroyed T 0 S gen 1kJ2W rev a N r 1h° f h h° T 0 s 2 r a N p 1h° f h h° T 0 s 2 pW rev a N r g 0,r a N p g 0,pW rev a N r 1g ° f g T 0 g °2 r a N p 1g ° f g T 0 g °2 p(15–25)(15–26)where g – f ° is the Gibbs function of formation (g – f ° 0 for stable elements likeN 2 and O 2 at the standard reference state of 25°C and 1 atm, just like theenthalpy of formation) and g – T 0 g – ° represents the value of the sensibleGibbs function of a substance at temperature T 0 relative to the standardreference state.For the very special case of T react T prod T 0 25°C (i.e., the reactants,the products, and the surroundings are at 25°C) and the partial pressureP i 1 atm for each component of the reactants and the products, Eq. 15–26reduces toW rev a N r g ° f,r a n p g ° f,p 1kJ2(15–27)We can conclude from the above equation that the g – ° f value (the negativeof the Gibbs function of formation at 25°C and 1 atm) of a compoundrepresents the reversible work associated with the formation of that compoundfrom its stable elements at 25°C and 1 atm in an environment at25°C and 1 atm (Fig. 15–31). The g – ° f values of several substances are listedin Table A–26.ExergyChapter 15 | 775ReactantsReversibleworkProductsT, P StateFIGURE 15–30The difference between the exergyof the reactants and of the productsduring a chemical reaction is thereversible work associated with thatreaction.T 0 = 25°CStableelements25°C,1 atmC + O 2 → CO 225°C,1 atmCompound25°C,1 atmW rev = – g– f ° , CO2 = 394,360 kJ/ J/kmolFIGURE 15–31The negative of the Gibbs function offormation of a compound at 25C, 1atm represents the reversible workassociated with the formation of thatcompound from its stable elements at25C, 1 atm in an environment that isat 25C, 1 atm.