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Exergy

Exergy. Thermodynamics Professor Lee Carkner Lecture 15. PAL # 14 Reversibility. Air compressed with constant specific heats R = 0.287 (Table A-1), k = 1.4 (Table A-2) (T 2 /T 1 ) = (P 2 /P 1 ) (k-1)/k T 2 = T 1 (P 2 /P 1 ) (k-1)/k = (290)(800/100) (0.4/1.4) = 525.3 K

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Exergy

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  1. Exergy Thermodynamics Professor Lee Carkner Lecture 15

  2. 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 = Du = cvDT = 0.727(525.3-290) =

  3. 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) =

  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 • 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 • 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 • hII = • Work consuming devices • hII = • Refrigerators • hII = • 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 • Exam #2 Wednesday, April 19 • Read: 8.6-8.8 • Homework: Ch 8, P: 38, 42, 64, 75

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