Explanation Write the energy balance equation using steady-flow equation. E in − E out = Δ E system (I) Here, the total energy entering the system is E in , the total energy leaving the system is E out , and the change in the total energy of the system is Δ E system . Substitute 0 for E in , − Q out for E out , and Δ U for Δ E system in Equation (I) ( 0 ) − Q out = Δ U − Q out = ∑ N P ( h ¯ f ° + h ¯ − h ¯ ° ) P − ∑ N R ( h ¯ f ° + h ¯ − h ¯ ° ) R − Q out = ∑ N P ( h ¯ f ° + h ¯ 350 K − h ¯ 298 K ° ) P − ∑ N R ( h ¯ f ° ) R (II) Here, the enthalpy of formation for product is h ¯ f , P ° , the enthalpy of formation for reactant is h ¯ f , R ° , the mole number of the product is N P , and the mole number of the reactant is N R . Calculate the molar mass of the C 8 H 18 . M C 8 H 18 = [ ( N C ) ( M C ) + ( N H ) ( M H ) ] (III) Here, the number of carbon atoms is N C , the molar mass of the carbon is M C , the number of hydrogen atoms is N H , the molar mass of the hydrogen is M H . Write the expression for entropy generation during this process. S gen = S P − S R + Q out T surr (IV) Write the combustion equation of Equation (VI) S gen = S P − S R + Q out T surr → S gen = ∑ N P s ¯ P − ∑ N R s ¯ R + Q out T surr (V) Here, the entropy of the product is s ¯ P , the entropy of the reactant is s ¯ R , the heat transfer for C 8 H 18 is Q out , and the surrounding temperature is T surr . Determine the entropy at the partial pressure of the components. S i = N i s ¯ i ( T , P i ) = N i s ¯ i ° ( T , P 0 ) − R u ln ( y i P m ) (VI). Here, the partial pressure is P i , the mole fraction of the component is y i , the total pressure of the mixture is P m , and the universal gas constant is R u . Write the expression for exergy destruction during this process. X destroyed = T 0 S gen (VII) Here, the thermodynamic temperature of the surrounding is T 0 Determine the maximum amount of work produced by automobile engine per unit mass. W max = X destory M C 8 H 18 (VIII) Here, the molar mass of the C 8 H 18 . Conclusion: Perform unit conversion of temperature at state 1 from degree Celsius to Kelvin. For air temperature enter in the machine, T enter = 25 °C = ( 25 + 273 ) K = 298 K For air temperature exit from the machine, T enter = 77 °C = ( 77 + 273 ) K = 350 K Write the combustion equation of 1 kmol for C 8 H 18 . { C 8 H 18 ( l ) + 3 a th ( O 2 + 3.76 N 2 ) } → { 8 CO 2 + 9 H 2 O + 2 a th O 2 + ( 3 ) ( 3.76 ) a th N 2 } (VIII) Here, liquid octane is C 8 H 18 , stoichiometric coefficient of air is a th , oxygen is O 2 , nitrogen is N 2 , carbon dioxide is CO 2 and water is H 2 O . Express the stoichiometric coefficient of air by O 2 balancing. 3 a th = 8 + 4.5 + 2 a th a th = 12.5 Substitute 12.5 for a th in Equation (VIII). { C 8 H 18 ( l ) + 3 ( 12.5 ) ( O 2 + 3.76 N 2 ) } → { 8 CO 2 + 9 H 2 O + 2 ( 12.5 ) O 2 + ( 3 ) ( 3.76 ) ( 12.5 ) N 2 } { C 8 H 18 ( l ) + 37.5 ( O 2 + 3.76 N 2 ) } → { 8 CO 2 + 9 H 2 O + 25 O 2 + ( 141 ) N 2 } (IX). Refer Appendix Table A-18, A-19, A-20, and A-23, obtain the enthalpy of formation, at 298 K , and 350 K for C 8 H 18 ( l ) , O 2 , N 2 , H 2 O ( g ) , and CO 2 is given in a table (I) as: Substance h ¯ f ° kJ / kmol h ¯ 298 K kJ / kmol h ¯ 350 K kJ / kmol C 8 H 18 ( l ) -249,950 --- --- O 2 0 8682 10,213 N 2 0 8669 10,180 H 2 O ( g ) -241820 9904 11,652 CO 2 -393,520 9364 11,351 Refer Equation (IX), and write the number of moles of reactants

CONNECT FOR THERMODYNAMICS: AN ENGINEERI

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Author: CENGEL

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Chapter 15.7, Problem 87P

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CONNECT FOR THERMODYNAMICS: AN ENGINEERI

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