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

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Author: CENGEL

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Chapter 15.7, Problem 88P

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Chapter 15.7, Problem 87P

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Octane gas (C8H18) and atmospheric air are supplied to a combustion chamber at 25°C at the stoichiometric air/fuel ratio. The combustion takes place adiabatically under steady-flow condition. The change in velocity and the work transfer can be assumed negligible. The Enthalpy of Combustion of octane gas at 25°C is – 5,116,180 kJ/kmol (when H2O in the combustion products is in vapor phase). Determine with aid of the Table on Page 26, the final temperature of the combustion products.

Liquid propane (C3H8) enters a combustion chamber at 25°C at a rate of 0.07 kg/min where it is mixed and burned with 40 percent excess air that enters the combustion chamber at 7°C. An analysis of the combustion gases reveals that all the hydrogen in the fuel burns to H,0 but only 75 percent of the carbon burns to CO, with the remaining 25 percent forming CO. determine (a) the balanced equation for actual combustion process and (b) the mass flow rate of air.

Liquid propane (C3H8) enters a combustion chamber at 25°C at a rate of 0.05 kg/min where it is mixed and burned with 50 percent excess air that enters the combustion chamber at 7°C. An analysis of the combustion gases reveals that all the hydrogen in the fuel burns to H2O but only 90 percent of the carbon burns to CO2, with the remaining 10 percent forming CO. If the exit temperature of the combustion gases is 1500 K, determine 1-The balanced chemical equation for the actual process 2-Air- Fuel ratio 3-The mass flow rate of air

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Thermodynamics: An Engineering Approach

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