exergy thermodynamics professor lee carkner lecture 15
Post on 21-Dec-2015
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PAL # 14 Reversibility Air compressed with constant specific heats R = 0.287 (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) = 525.3 K
w = u = cvT = 0.727(525.3-290) =
PAL # 14 Reversibility Air compressed with non-constant specific
heats Need to use reduced pressure table (A-17) For T1 = 290, Pr1 = 1.2311 and u1 = 206.91
Pr2 = (P2/P1)Pr1 = (800/100)(1.2311) = 9.849
For table A-17 this corresponds to T2 = 522.4 K and u2 = 376.16
w = u2-u1 = (376.16-206.91) =
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
Exergy Systems
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
Kinds of Work Surroundings 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
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:
th,rev is the Carnot Efficiency
Efficiencies
Work producing devices II =
Work consuming devices II =
Refrigerators II =
General Definition II = xrecovered/xsupplied = 1 – (xdestroyed/xsupplied)
Exergy of a Closed System
The exergy per unit mass () is:
= (u-u0)+P0(v-v0)-T0(s-s0)+V2/2+gz
For a process we can subtract the exergies at the two states
= (u2-u1)+P0(v2-v1)-T0(s2-s1)+(V22-V2
1)/2+g(z2-z1)
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, :
= (h-h0)-T0(s-s0)+V2/2+gz Exergy change of a fluid stream is:
= (h2-h1)-T0(s2-s1)+(V22-V2
1)/2+g(z2-z1)
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
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.
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 =