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Energy Conversion

Energy Conversion. CHE 450/550. Ideal Gas Basics and Heat Capacities - I. Ideal gas: a theoretical gas composed of a set of non-interacting point particles. obeys the ideal gas law: PV= nRT R is “gas constant” [R = 8.314 J·K -1 ·mol -1 ] You may see R specific =R/MW [J·K -1 ·kg -1 ]

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Energy Conversion

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  1. Energy Conversion CHE 450/550

  2. Ideal Gas Basics and Heat Capacities - I Ideal gas: • a theoretical gas composed of a set of non-interacting point particles. • obeys the ideal gas law: PV=nRT • R is “gas constant” [R = 8.314 J·K-1·mol-1] • You may see Rspecific=R/MW [J·K-1·kg-1] • At close to normal conditions most real gases behave like an ideal gas. • Various relationships written. E.g.,

  3. Ideal Gas Basics and Heat Capacities - II Heat capacity “C” relates the change in temperature DT that occurs when an amount of heat DQ is added Usually given as per mass (specific heat capacity, c) [J.kg-1.K-1] The conditions under which heat is added play a role: • At constant volume, cV=(du/dt)V (no PV work performed during heating) • At constant pressure cP=(dh/dt)P (constant P, so as T increases, V increases: PV work performed) • A thermally perfect gas can be shown to have cP=cV+Rspecific (Sorry but it would take too long to go through the formal derivation of this)

  4. Ideal Gas Basics and Heat Capacities - III • An important quantity is k=cP/cV • known as the “adiabatic index” or “isentropic expansion factor” (you’ll also see it written as g gamma or k kappa) • Polytropic processes: PVN=constant (N = polytropic index) N = 0 (PV0 = P) an isobaric process (constant pressure) N = 1 (PV = nRT) an isothermal process (constant temperature) 1 < N < k A quasi-adiabatic process (real process) N = k since kis the adiabatic index, this is an adiabatic process (no heat transferred, all excess energy converted to PV work)   N=∞ Equivalent to an isochoric process (constant volume)

  5. PV and TS diagrams Some key terms: Isobar – “at the same pressure” Isochore – “at the same volume” Isotherm – “at the same temperature” Isentropic – “at the same entropy” Adiabatic – “without heat exchange (with the surroundings)” P T V S

  6. PV and TS diagrams – Isobar and Isochore Isobar – “at the same pressure” Isochore – “at the same volume” Where do those go on the PV and TS diagrams? P T V S

  7. PV and TS diagrams – Isotherm, Isentropic and Adiabatic Isotherm – “at the same temperature” Isentropic – “at the same entropy” Adiabatic – “without heat exchange (with the surroundings)” Where do those go on the PV and TS diagrams? P T V S

  8. TS diagram – Isobars with phase change Steam quality (fraction of fluid that is steam) • 0 < X < 1 • At X = 0 we have all fluid in liquid phase • At X = 1 we have all fluid in gas phase (pure steam)

  9. Rankine Cycle

  10. Rankine Cycle: Common Improvements • Increase supply pressure, decrease exhaust pressure • Superheat • Reheat • Feedwater Heater • open/closed

  11. Solar Thermal Power Plant Ausra (Bakersfield, CA, 10/2008)Direct Steam Generation

  12. Brayton Cycle http://commons.wikimedia.org/wiki/File:Brayton_cycle.svg

  13. Ideal Brayton Cycle Analysis Open system energy balance based on enthalpy

  14. Ideal Brayton Cycle Analysis

  15. Ideal Brayton Cycle Analysis Efficiency is function of compression ratio!

  16. Brayton Cycle: Common Improvements • Increase Compression Ratio • Also increases air temperature coming out of compressor (bad) (Karlekar, 1983) (Segal, 2003)

  17. Actual processes are not isentropic Turbines, Compressors, generators can be highly efficient (>80%) Example: A compressor has an isentropic efficiency of 85%, meaning that the actual work required is 1/0.85 times that of an isentropic process. “a” “b” Wcompressor

  18. Improving efficiency • Intercooling and Reheat • Allows for higher compression ratios • Cool before compression, reheat during/between expansion • Regeneration • Heat the compressed air with turbine exhaust

  19. Combined Cycle Power Plant

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