1. Thermodynamics Lecture Series email: drjjlanita@hotmail.com http://www.uitm.edu.my/faculties/fsg/drjj1.h tmldrjjlanita@hotmail.com Applied Sciences Education Research Group (ASERG) Faculty of Applied Sciences Universiti Teknologi MARA Gas Mixtures – Properties and Behaviour

2. Review – Steam Power Plant Pump Boiler Turbin e Condenser High T Res., T H Furnace q in = q H  in  out Low T Res., T L Water from river A Schematic diagram for a Steam Power Plant q out = q L Working fluid: Water q in - q out =  out -  in q in - q out =  net,out

3. Review - Steam Power Plant Steam Power Plant High T Res., T H Furnace q in = q H  net,out Low T Res., T L Water from river An Energy-Flow diagram for a SPP q out = q L Working fluid: Water Purpose: Produce work, W out,  out

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

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

6. Entropy Balance –Steady-flow device Review - Entropy Balance Heat exchanger: energy balance; Assume  ke mass = 0,  pe mass = 0 where Q in Case 1

7. Entropy Balance –Steady-flow device Review - Entropy Balance Heat exchanger: energy balance; Assume  ke mass = 0,  pe mass = 0 where Q in Case 1 Case 2

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

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

10. T- s diagram for an Ideal Rankine Cycle Vapor Cycle – Ideal Rankine Cycle T,  C s, kJ/kg  K 1 2 T crit THTH T L = T sat@P4 T sat@P2 s 3 = s 4 s 1 = s 2 q in = q H 4 3 PHPH PLPL  in  out pump q out = q L condenser turbine boiler s 1 = s f@P1 h 1 = h f@P1 s 3 = s @P3,T3 s 4 = [s f +xs fg ] @P4 = s 3 h 3 = h @P3,T3 h 4 = [h f +xh fg ] @P4 h 2 = h 1 + 2 (P 2 – P 1 ); where Note that P 1 = P 4

11. Review – Ideal Rankine Cycle Energy Analysis Efficiency

12. Review – Reheat Rankine Cycle Pump Boiler Hig h P turb ine Condenser High T Reservoir, T H q in = q H  in  out,1 q out = q L Low T Reservoir, T L Lo w P turb ine  out,2 1 2 3 4 5 6 q reheat

13. Reheating increases  and reduces moisture in turbine Review – Reheat Rankine Cycle T L = T sat@P1  in s 5 = s 6 s 1 = s 2 T crit THTH T sat@P4 T sat@P3 s 3 = s 4 q out = h 6 -h 1  out, II P 4 = P 5 P 6 = P 1 6 1 5 4 q reheat = h 5 -h 4 q primary = h 3 -h 2  out P3P3 3 2 T,  C s, kJ/kg  K s 6 = [s f +xs fg ] @P6. Use x = 0.896 and s 5 = s 6 h 6 = [h f +xh fg ] @P6

14. Energy Analysis Review – Reheat Rankine Cycle q in = q primary + q reheat = h 3 - h 2 + h 5 - h 4 q out = h 6 -h 1  net,out =  out,1 +  out,2 = h 3 - h 4 + h 5 - h 6

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

16. Non-reacting gas mixtures as working fluid Gas Mixtures – Ideal Gases  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, CO 2, CH 4 (methane), C 3 H 8 (Propane)

17. Ideal Gases Gas Mixtures – Ideal Gases  Low density (mass in 1 m 3 ) gases Molecules are further apart  Real gases satisfying condition P gas > T crit P gas > T crit, have low density and can be treated as ideal gases High density Low density Molecules far apart

18. Ideal Gases Gas Mixtures – Ideal Gases  Equation of State  Equation of State - P- -T behaviour P =RT R T P =RT (energy contained by 1 kg mass) where is the specific volume in m 3 /kg, R is gas constant, kJ/kg  K, T is absolute temp in Kelvin. High density Low density Molecules far apart

19. Ideal Gases Gas Mixtures – Ideal Gases  Equation of State  Equation of State - P- -T behaviour P =RT P =RT, since = V/m then, P(V/m)=RT. So, PV =mRT PV =mRT, in kPa  m 3 =kJ. Total energy of a system. Low density High density

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

21. Ideal Gases Gas Mixtures – Ideal Gases  Equation of State  Equation of State for mixtures P mix mix =R mix T mix P mix V mix =m mix R mix T mix P mix mix =R mix T mix, P mix V mix =m mix R mix T mix P mix V mix = N mix R u T mix m mix = M mix N mix P mix V mix = N mix R u T mix where m mix = M mix N mix R mix R mix is apparent or mixture gas constant, kJ/kg  K, T mix N mix T mix is absolute temp in Kelvin, N mix is no of kilomoles, M mix M mix is molar mass of mixture in kJ/kmole and R u R u =MR R u is universal gas constant; R u =MR. R u = 8.314 kJ/kmol  K

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

23. Gravimetric Analysis Gas Mixtures – Composition by Mass  Composition by weight or mass  Mass of components add to the total mass of mixtures + 6 kg H2H2 O2O2 32 kg + == 38 kg H 2 +O 2 Mass fraction of components

24. Volumetric Analysis Gas Mixtures – Composition by Moles  Composition by kilomoles  Number of kilomoles of components add to the total number of kilomoles of mixtures + 3 kmol H2H2 O2O2 1 kmol + == 4 kmol H 2 +O 2 Number of kilomoles is Hence,

25. Volumetric Analysis Gas Mixtures – Composition by Moles + 3 kmol H2H2 O2O2 1 kmol + == 4 kmol H 2 +O 2 Mole fraction of components Hence

26. Composition Summary Gas Mixtures – Composition by Moles + 3 kmol H2H2 O2O2 1 kmol + == 4 kmol H 2 +O 2 Gravimetric Analysis Volumetric Analysis where

27. Dalton’s Law Gas Mixtures – Additive Pressure P H2 H2H2 O2O2 P O2 + + == P H2 + P O2 H 2 +O 2  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. Amagat’s Law Gas Mixtures – Additive Volume  The total volume occupied in a container at pressure P mix and absolute temperature T mix, is the sum of component volumes occupied by each gas in that container at P mix, T mix. k is total number of components V H2 H2H2 O2O2 V O2 + + == V H2 + V O2 H 2 +O 2

29. Partial Pressure Gas Mixtures –Pressure Fraction  The pressure fraction for each gas inside the container is H 2 +O 2 Hence the partial pressure is In general, Since

30. Partial Volume Gas Mixtures –Volume Fraction  The volume fraction for each gas inside the container is H 2 +O 2 Hence the partial volume is In general, Since