study problems ch12

# study problems ch12 - Sonntag/Borgnakke Study problems...

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Sonntag/Borgnakke Study problems chapter 12 CHAPTER 12 STUDY PROBLEMS MIXTURES Mixtures of ideal gases Moist air The psychrometric chart FUNDAMENTALS of Thermodynamics Sixth Edition SONNTAG BORGNAKKE VAN WYLEN

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Sonntag/Borgnakke Study problems chapter 12 12.1 Mixing in a rigid tank A mixture of carbon dioxide and oxygen is made by having a rigid tank containing two sections separated by a membrane. In A we have 1 kg CO 2 at 1000 K and in B we have 2 kg O 2 at 300 K both at 200 kPa. The membrane is broken and the mixture comes to a uniform state without any external heat transfer. What is the final temperature and what are the final partial pressures. C.V. The whole tank. Energy Eq.5.11: U 2 - U 1 = 0 = m CO 2 C V0 (T 2 - T A1 ) + m O 2 C V0 (T 2 - T B1 ) V A = m CO 2 RT A1 /P = 1 × 0.1889 × 1000/ 200 = 0.9445 m 3 V B = m O 2 RT B1 /P = 2 × 0.2598 × 300 / 200 = 0.7794 m 3 Continuity Eq.: m 2 = m CO 2 + m O 2 = 3 kg Energy Eq.: 1 × 0.653 (T 2 - 1000) + 2 × 0 .662 (T 2 - 300) = 0 Solving, T 2 = 531.2 K R mix = Σ c i R i = 1 3 × 0.1889 + 2 3 × 0.2598 = 0.2362 kJ/kg K P 2 = m 2 RT 2 /(V A +V B ) = 3 × 0.2362 × 531.2 / 1.5588 = 241.5 kPa B A Comment: We could also have used values of u from Table A.8 to write U 2 = (mu) CO 2 + (mu) O 2 = U 1 = 1 × 782.75 + 2 × 195.2 = 1173.15 kJ But now it becomes trial and error to find the single T 2 . Guess a T 2 and look in A.8 U 2 at 550 K = 349.12 + 2 × 367.7 = 1084.5 kJ; This is too low U 2 at 600 K = 392.72 + 2 × 404.46 = 1201.6 kJ This a little too high Interpolate to get: T 2 = 550 + 50 (1173.15 – 1084.5)/(1201.6 – 1084.5) = 588 K Notice here we got a T 2 that is 10% higher than before so we should have used a higher average value for the heat capacity for CO 2 .
Sonntag/Borgnakke Study problems chapter 12 12.2 Mixing in a flow setup A mixture of carbon dioxide and oxygen is made by having a flow of 1 kmol/s CO 2 at 1000 K, 200 kPa mix with a flow of 2 kmol/s O 2 at 300 K, 200 kPa. The exit mixture has a uniform state at 200 kPa total pressure and there is no external heat transfer and no significant kinetic energy. What is the exit temperature and what are the partial pressures

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## This note was uploaded on 10/20/2009 for the course MECHENG MEecheng 3 taught by Professor Borgnakke during the Fall '09 term at University of Michigan.

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study problems ch12 - Sonntag/Borgnakke Study problems...

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