Explanation Express the theoretical combustion equation of octane with stoichiometric amount of air. C 8 H 18 ( g ) + a th ( O 2 + 3.76 N 2 ) → 8 CO 2 + 9 H 2 O + 3.76 a th N 2 (I) Here, octane gas 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. a th = 8 + 4.5 = 12.5 Substitute 12.5 for a th in Equation (I). C 8 H 18 ( g ) + 12.5 ( O 2 + 3.76 N 2 ) → 8 CO 2 + 9 H 2 O + 3.76 × 12.5 N 2 C 8 H 18 ( g ) + 12.5 ( O 2 + 3.76 N 2 ) → 8 CO 2 + 9 H 2 O + 47 N 2 (II) Express the heat transfer from the combustion chamber. − Q ¯ out = ∑ N P ( h ¯ f o + h ¯ − h ¯ o ) P − ∑ N R ( h ¯ f o + h ¯ − h ¯ o ) R = ∑ N P ( h ¯ f o + h ¯ 1000 K − h ¯ 298 K o ) P − ∑ N R ( h ¯ f o ) R (III) Here, number of moles of products is N P , number of moles of reactants is N R , enthalpy of formation is h ¯ f . Express total mole numbers initially present in the combustion chamber from ideal gas relation. N 1 = P 1 ν 1 R a T 1 (IV) Here, initial pressure is P 1 , initial volume is ν 1 , universal gas constant of air is R a and initial temperature is T 1 . Express the amount of moles of octane burned. N C 8 H 18 , burned = N 1 1 + 12.5 N air (V) Here, number of moles of air is N air . Express the heat transfer from the combustion chamber during this process. Q out = N C 8 H 18 , burned Q ¯ out (VI) Conclusion: Refer Equation (II), and write the number of moles of products. N P , CO 2 = 8 kmol N P , H 2 O = 9 kmol N P , N 2 = 47 kmol Here, number of moles of product carbon dioxide, water, and nitrogen is N P , CO 2 , N P , H 2 O , and N P , N 2 respectively. Refer Equation (II), and write the number of moles of reactant. N R , C 8 H 18 = 1 kmol Here, number of moles of product octane is N R , C 8 H 18 . Perform unit conversion of temperature at state 1 from degree Celsius to Kelvin. T 1 = 25 °C = ( 25 + 273 ) K = 298 K Refer Appendix Table A-18, A-19, A-20, A-23 and A-26 and write the property table for products and reactants as in Table (1)

8th Edition

ISBN: 9780073398174

Author: Yunus A. Cengel Dr., Michael A. Boles

Publisher: McGraw-Hill Education

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Chapter 15.7, Problem 68P

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