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 = J·K -1 ·mol -1 ] You may see R specific =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  T that occurs when an amount of heat  Q 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, c V =(du/dt) V (no PV work performed during heating) – At constant pressure c P =(dh/dt) P (constant P, so as T increases, V increases: PV work performed) – A thermally perfect gas can be shown to have c P =c V +R specific (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=c P /c V – known as the “adiabatic index” or “isentropic expansion factor” (you’ll also see it written as  gamma or  kappa) Polytropic processes: PV N =constant (N = polytropic index) N = 0 (PV 0 = 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 k is 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)

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)” PV and TS diagrams P V T S

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

PV and TS diagrams – Isotherm, Isentropic and Adiabatic P V T S 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?

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

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

Heat Recovery Steam Generator GE Power Systems

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

EU SOLGATE

Brayton Cycle

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. W compressor “a” “b”

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

Combined Cycle Power Plant

Briefly: Why Fuel Cells? H 2 (g), O 2 (g)H 2 O (g) W rev Q out Fuel Cell

CHP/Cogeneration

CHP Appropriate in some places (cities, large buildings, universities), though misleading Heat is not a “free by-product”, as producing heat takes away from producing electricity Don’t “add” efficiencies, instead, calculation utilization, ε :