1. Energy Conversion
CHE 450/550

2. 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 = 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

3. 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

4. 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

5. 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

6. TS diagram – Isobars with phase change

7. 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)

8. 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.

9. Brayton Cycle

10. Ideal Brayton Cycle Analysis
Open system energy balance uses enthalpy

11. Ideal Brayton Cycle Analysis

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

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

14. 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”

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

17. 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)

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

19. Rankine Cycle

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

21. Combined Cycle Power Plant

22. Heat Recovery Steam Generator
GE Power Systems

23. CHP/Cogeneration

24. 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 :

25. EU SOLGATE

26. EU SOLGATE

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

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