1. Thermodynamics Professor Lee Carkner Lecture 15
Exergy
Thermodynamics
Professor Lee Carkner
Lecture 15

2. PAL # 14 Reversibility Air compressed with constant specific heats
R = (Table A-1), k = 1.4 (Table A-2)
(T2/T1) = (P2/P1)(k-1)/k
T2 = T1(P2/P1)(k-1)/k = (290)(800/100)(0.4/1.4) = K
w = Du = cvDT = 0.727( ) =

3. PAL # 14 Reversibility Air compressed with non-constant specific heats
Need to use reduced pressure table (A-17)
For T1 = 290, Pr1 = and u1 =
Pr2 = (P2/P1)Pr1 = (800/100)(1.2311) = 9.849
For table A-17 this corresponds to T2 = K and u2 =
w = u2-u1 = ( ) =

4. Exergy
Exergy (x) is a measure of the work potential of an energy source
Defined as:
The dead state is defined as the state in thermodynamic equilibrium with the environment
Exergy is the upper limit for the work an actual device could produce

5. Exergy Systems Kinetic energy Potential Energy
e.g. the amount of work you can generate from a geothermal well depends on where you dump the waste heat
Kinetic energy
Potential Energy
Both KE and PE can be completely converted to work
n.b. V and z are relative to the environment

6. Kinds of Work Surroundings Work Useful work Reversible work
Wsurr = P0(V2-V1)
Useful work
Wa = W – P0(V2-V1)
Reversible work
If the final state is the dead state the reversible work equals the exergy
Irreversibility
I = Wrev - Wu

7. Second Law Efficiency
Our standard thermal efficiency has 100% as an upper limit
We instead want to compare the work output to the true maximum; that given by a reversible engine
The second law efficiency is:
hth,rev is the Carnot Efficiency

8. Comparing With Efficiency

9. Efficiencies Work producing devices Work consuming devices
hII =
Work consuming devices
Refrigerators
General Definition
hII = xrecovered/xsupplied = 1 – (xdestroyed/xsupplied)

10. Exergy of a Closed System
The exergy per unit mass (f) is:
f = (u-u0)+P0(v-v0)-T0(s-s0)+V2/2+gz
For a process we can subtract the exergies at the two states
Df = (u2-u1)+P0(v2-v1)-T0(s2-s1)+(V22-V21)/2+g(z2-z1)

11. Flow Exergy
The flow energy is Pv and we can find its exergy by subtracting the work needed to displace the fluid against the atmosphere
By including this in our previous relationship we find the flow or stream exergy, y:
y = (h-h0)-T0(s-s0)+V2/2+gz
Exergy change of a fluid stream is:
Dy = (h2-h1)-T0(s2-s1)+(V22-V21)/2+g(z2-z1)

12. Exergy Transfer: Heat
The most work that a given amount of heat can generate is through a Carnot cycle, so we can use the reversible efficiency to find the exergy:
Where T0 is the temperature of the environment

13. Transferring Exergy

14. Exergy Transfer: Work
One exception is overcoming atmospheric pressure for moving boundary work
Xwork = W – Wsurr = W – P0(V2-V1)
e.g. shaft work, electrical work, etc.

15. Exergy Transfer: Mass
Mass flow carries exergy into or out of a system just as it does energy
May have to integrate if fluid properties are variable
Xmass =
Xheat =

16. Next Time Next class Tuesday, April 18 Read: 8.6-8.8
Exam #2 Wednesday, April 19
Read:
Homework: Ch 8, P: 38, 42, 64, 75