Thermodynamics Professor Lee Carkner Lecture 15 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) (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) =

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 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

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

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

Comparing With Efficiency

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

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)

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)

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

Transferring Exergy

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 =

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