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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 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 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.,
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)
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)
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
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
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
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)
Rankine Cycle: Common Improvements • Increase supply pressure, decrease exhaust pressure • Superheat • Reheat • Feedwater Heater • open/closed
Solar Thermal Power Plant Ausra (Bakersfield, CA, 10/2008)Direct Steam Generation
Brayton Cycle http://commons.wikimedia.org/wiki/File:Brayton_cycle.svg
Ideal Brayton Cycle Analysis Open system energy balance based on enthalpy
Ideal Brayton Cycle Analysis Efficiency is function of compression ratio!
Brayton Cycle: Common Improvements • Increase Compression Ratio • Also increases air temperature coming out of compressor (bad) (Karlekar, 1983) (Segal, 2003)
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
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
