Thermodynamics

calculating the h of a reaction from a knowledge of K P , which is easier toChapter 16 | 807This equation has two important implications. First, it provides a means ofRdetermine. Second, it shows that exothermic reactions 1h R 6 02 such asReaction: C + O 2 → CO 2combustion processes are less complete at higher temperatures since K PT, K Kdecreases with temperature for such reactions (Fig. 16–16).PRh R Solution The at a specified temperature is to be determined using theEstimate the enthalpy of reaction h for the combustion process of hydrogen4000EXAMPLE 16–6 The Enthalpy of Reactionof a Combustion ProcessH 2 + 0.5O 2 → H 2 O at 2000 K, using (a) enthalpy data and (b) K P data.enthalpy and K p data.Assumptions Both the reactants and the products are ideal gases.Analysis (a) The h R of the combustion process of H 2 at 2000 K is the amountof energy released as 1 kmol of H 2 is burned in a steady-flow combustionchamber at a temperature of 2000 K. It can be determined from Eq. 15–6,h R a N p 1h f ° h h°2 p a N r 1h f ° h h°2 r1000200030004.78 10 202.25 10 107.80 10 61.41 10 5FIGURE 16–16Exothermic reactions are lesscomplete at higher temperatures. N H2 O 1h f ° h 2000 K h 298 K 2 H2 O N H21h f ° h 2000 K h 298 K 2 H2N O21h f ° h 2000 K h 298 K 2 O2Substituting yieldsh R 11 kmol H 2 O231241,820 82,593 99042 kJ>kmol H 2 O4(b) The h R value at 2000 K can be estimated by using K P values at 1800and 2200 K (the closest two temperatures to 2000 K for which K P data areavailable) from Table A–28. They are K P1 18,509 at T 1 1800 K andK P2 869.6 at T 2 2200 K. By substituting these values into Eq. 16–18,the value is determined to beh R 11 kmol H 2 2310 61,400 84682 kJ>kmol H 2 4 10.5 kmol O 2 2310 67,881 86822 kJ>kmol O 2 4 251,663 kJ/kmollnlnK P2K P1 h RR ua 1 T 1 1 T 2b869.618,509 h R8.314 kJ>kmol # K a 11800 K 12200 K bh R 251,698 kJ/kmolDiscussion Despite the large temperature difference between T 1 and T 2(400 K), the two results are almost identical. The agreement between thetwo results would be even better if a smaller temperature interval were used.