Energy Conversion CHE 450/550

Ideal Gas Basics and Heat Capacities - I 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. Most useful

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 V T S

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

TS diagram – Isobars with phase change

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) In general cV and cP are functions of kinetic energy of molecules forming a material (translational, vibrational, rotational), and intra- and intermolecular forces.

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

Ideal Brayton Cycle Analysis Open system energy balance uses enthalpy

Ideal Brayton Cycle Analysis

Ideal Brayton Cycle Analysis Use Polytropic relations Efficiency is function of compression ratio

Ideal Brayton Cycle Analysis Use Polytropic relations Efficiency is function of compression ratio

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. Wcompressor “a” “b”

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

Intercooling and Reheat Allows for higher compression ratios Cool before compression, reheat during/between expansion Regeneration Heat the compressed air with turbine exhaust (Karlekar, 1983)

Briefly: Why Fuel Cells? Wrev H2 (g), O2 (g) H2O (g) Fuel Cell Qout

Rankine Cycle

Rankine Cycle: Common Improvements Increase supply pressure, decrease exhaust pressure Superheat Reheat Feedwater Heater open/closed (Karlekar, 1983)

Combined Cycle Power Plant

Heat Recovery Steam Generator GE Power Systems

CHP/Cogeneration http://www.eesi.org/files/images/cornell_chp.jpg

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 :

EU SOLGATE

EU SOLGATE

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

A conceptual heat engine…. (Funk, 1966) (Teo et al., 2005)