Thermodynamics Lecture Series

1. Thermodynamics Lecture Series Assoc. Prof. Dr. J.J. Gas Mixtures – Properties and Behaviour Applied Sciences Education Research Group (ASERG) Faculty of Applied Sciences Universiti Teknologi MARA email: drjjlanita@hotmail.comhttp://www.uitm.edu.my/faculties/fsg/drjj1.html

2. Review – Steam Power Plant High T Res., TH Furnace Working fluid: Water qin = qH Boiler Turbine out Pump in Condenser qout = qL qin- qout = out - in Low T Res., TL Water from river qin- qout = net,out A Schematic diagram for a Steam Power Plant

3. Review - Steam Power Plant High T Res., TH Furnace Working fluid: Water Purpose: Produce work, Wout, out qin = qH Steam Power Plant net,out qout = qL Low T Res., TL Water from river An Energy-Flow diagram for a SPP

4. Review - Steam Power Plant Thermal Efficiency for steam power plants For real engines, need to find qL and qH.

5. 3, Hot water inlet 1 Qin Cold water Inlet 2 Out 4 Review - Entropy Balance Entropy Balance –Steady-flow device Heat exchanger Case 1 – blue border Case 2 – red border

6. Qin Review - Entropy Balance Entropy Balance –Steady-flow device Heat exchanger: energy balance; where Assume kemass = 0, pemass = 0 Case 1

7. Qin Review - Entropy Balance Entropy Balance –Steady-flow device Heat exchanger: energy balance; where Assume kemass = 0, pemass = 0 Case 1 Case 2

8. Qin Review - Entropy Balance Entropy Balance –Steady-flow device Heat exchanger: Entropy Balance where Case 1

9. Qin Review - Entropy Balance Entropy Balance –Steady-flow device Heat exchanger: Entropy Balance where Case 2

10. T, C 3 TH turbine boiler PH Tcrit qin = qH PL out Tsat@P2 2 TL= Tsat@P4 1 4 qout = qL in s, kJ/kgK pump s1 = s2 condenser s3 = s4 Vapor Cycle – Ideal Rankine Cycle Note that P1 = P4 s1 = sf@P1 h1 = hf@P1 T- s diagram for an Ideal Rankine Cycle s3 = s@P3,T3 h3 = h@P3,T3 s4 = [sf +xsfg]@P4 = s3 h4 = [hf +xhfg]@P4 h2 = h1 +2(P2 – P1); where

11. Review – Ideal Rankine Cycle Energy Analysis Efficiency

12. 3 2 4 5 1 6 Review – Reheat Rankine Cycle High T Reservoir, TH qin = qH High P turbine Boiler out,1 Pump qreheat in Low P turbine out,2 Condenser qout = qL Low T Reservoir, TL

13. T, C 3 5 TH qprimary = h3-h2 P4 = P5 P3 Tcrit out Tsat@P3 out, II P6 = P1 Tsat@P4 2 TL= Tsat@P1 1 6 qout = h6-h1 in s, kJ/kgK s5 = s6 s3 = s4 s1 = s2 Review – Reheat Rankine Cycle Reheating increases  and reduces moisture in turbine s6 = [sf +xsfg]@P6. Use x = 0.896 and s5 = s6 qreheat = h5-h4 h6 = [hf +xhfg]@P6 4

14. Review – Reheat Rankine Cycle Energy Analysis q in = qprimary + qreheat = h3 - h2 + h5 - h4 qout = h6-h1 net,out = out,1 + out,2 = h3 - h4 + h5 - h6

15. Gas Mixtures – Ideal Gases Vapor power cycles – Rankine cycle • Water as working fluid • cheap • Easily available • High latent heat of vaporisation, hfg. • Use property table to determine properties

16. Gas Mixtures – Ideal Gases Non-reacting gas mixtures as working fluid • Properties depends on • Components (constituents) of mixtures • Amount of each component • Volume of each component Pressure each component exerts on container walls • Extended properties may not be tabulated • Treat mixture as pure substances • Examples: Air, CO2, CH4 (methane), C3H8 (Propane)

17. High density Low density Molecules far apart Gas Mixtures – Ideal Gases Ideal Gases • Low density (mass in 1 m3) gases Molecules are further apart • Real gases satisfying condition Pgas << Pcrit; Tgas >> Tcrit , have low density and can be treated as ideal gases

18. Gas Mixtures – Ideal Gases Ideal Gases • Equation of State - P--T behaviour P=RT (energy contained by 1 kg mass) where  is the specific volume in m3/kg, R is gas constant, kJ/kgK, T is absolute temp in Kelvin. High density Low density Molecules far apart

19. Gas Mixtures – Ideal Gases Ideal Gases • Equation of State - P--T behaviour P=RT , since = V/m then, P(V/m)=RT. So, PV =mRT, in kPam3=kJ. Total energy of a system. High density Low density

20. Gas Mixtures – Ideal Gases Ideal Gases • Equation of State - P--T behaviour PV =mRT = NMRT = N(MR)T Hence, can also write PV = NRuT where N is no of kilomoles, kmol, M is molar mass in kg/kmole and Ru is universal gas constant; Ru=MR. Ru = 8.314 kJ/kmolK High density Low density

21. Gas Mixtures – Ideal Gases Ideal Gases • Equation of State for mixtures Pmixmix=RmixTmix , PmixVmix =mmixRmixTmix PmixVmix = NmixRuTmix where mmix = MmixNmix Rmix is apparent or mixture gas constant, kJ/kgK, Tmix is absolute temp in Kelvin, Nmix is no of kilomoles, Mmix is molar mass of mixture in kJ/kmole and Ru is universal gas constant; Ru=MR. Ru = 8.314 kJ/kmolK

22. Mass is , in kg Number of kilomoles is , in kmole Gas Mixtures – Ideal Gases Composition of gas mixtures • Specify by mass (gravimetric analysis) or volume ( volumetric or molar analysis) mass = Molar mass * Number of kilomoles

23. O2 H2 + + 6 kg 32 kg H2 +O2 = = 38 kg Gas Mixtures – Composition by Mass Gravimetric Analysis • Composition by weight or mass • Mass of components add to the total mass of mixtures Mass fraction of components

24. O2 H2 + + 3 kmol 1 kmol H2 +O2 = = 4 kmol Gas Mixtures – Composition by Moles Volumetric Analysis • Composition by kilomoles • Number of kilomoles of components add to the total number of kilomoles of mixtures Number of kilomoles is Hence,

25. O2 H2 + + 3 kmol 1 kmol H2 +O2 = = 4 kmol Gas Mixtures – Composition by Moles Volumetric Analysis Mole fraction of components Hence

26. O2 H2 + + 3 kmol 1 kmol H2 +O2 = = 4 kmol Gas Mixtures – Composition by Moles Composition Summary Gravimetric Analysis where Volumetric Analysis where

27. O2 H2 + + PH2 PO2 H2 +O2 = = PH2+ PO2 Gas Mixtures – Additive Pressure Dalton’s Law • The total pressure exerted in a container at volume V and absolute temperature T, is the sum of component pressure exerted by each gas in that container at V, T. k is total number of components

28. O2 H2 + + VH2 VO2 H2 +O2 = = VH2+ VO2 Gas Mixtures – Additive Volume Amagat’s Law • The total volume occupied in a container at pressure Pmix and absolute temperature Tmix, is the sum of component volumes occupied by each gas in that container at Pmix, Tmix. k is total number of components

29. H2 +O2 Gas Mixtures –Pressure Fraction Partial Pressure Since • The pressure fraction for each gas inside the container is Hence the partial pressure is In general,

30. H2 +O2 Gas Mixtures –Volume Fraction Partial Volume Since • The volume fraction for each gas inside the container is Hence the partial volume is In general,