1 / 21

Phase Transitions

Phase Transitions. Physics 313 Professor Lee Carkner Lecture 22. Exercise #21 Joule-Thomson. Joule-Thomson coefficient for ideal gas m = 1/c P [T( v/T) P -v] ( v/T) P = R/P m = 1/c P [(TR/P)-v] = 1/c P [v-v] = 0 Can J-T cool an ideal gas T does not change

talisha
Download Presentation

Phase Transitions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Phase Transitions Physics 313 Professor Lee Carkner Lecture 22

  2. Exercise #21 Joule-Thomson • Joule-Thomson coefficient for ideal gas • m = 1/cP[T(v/T)P-v] • (v/T)P = R/P • m = 1/cP[(TR/P)-v] = 1/cP[v-v] = 0 • Can J-T cool an ideal gas • T does not change • How do you make liquid He? • Use LN to cool H below max inversion temp • Use liquid H to cool He below max inversion temp

  3. First Order Phase Transitions • Consider a phase transition where T and P remain constant • If the molar entropy and volume change, then the process is a first order transition

  4. Phase Change • Consider a substance in the middle of a phase change from initial (i) to final (f) phases • Can write equations for properties as the change progresses as: • Where x is fraction that has changed

  5. Clausius - Clapeyron Equation • Consider the first T ds equation, integrated through a phase change T (sf - si) = T (dP/dT) (vf - vi) • This can be written: • But H = VdP + T ds, so the isobaric change in molar entropy is T ds, yielding: dP/dT = (hf - hi)/T (vf -vi)

  6. Phase Changes and the CC Eqn. • The CC equation gives the slope of curves on the PT diagram • Amount of energy that needs to be added to change phase

  7. Changes in T and P • For small changes in T and P, the CC equation can be written: • or: DT = [T (vf -vi)/ (hf - hi) ] DP

  8. Control Volumes • Often we consider the fluid only when it is within a container called a control volume • What are the key relationships for control volumes?

  9. Mass Conservation • Rate of mass flow in equals rate of mass flow out (note italics means rate (1/s)) • For single stream m1 = m2 • where v is velocity, A is area and r is density

  10. Energy of a Moving Fluid • The energy of a moving fluid (per unit mass) is the sum of the internal, kinetic, and potential energies and the flow work • Total energy per unit mass is: • Since h = u +Pv q = h + ke +pe (per unit mass)

  11. Energy Balance • Rate of energy transfer in is equal to rate of energy transfer out for a steady flow system: • For a steady flow situation: Sin[Q + W + mq] = Sout [Q + W + mq] • In the special case where Q = W = ke = pe = 0

  12. Application: Mixing Chamber • In general, the following holds for a mixing chamber: • Mass conservation: • Energy balance: • Only if Q = W = pe = ke = 0

  13. Open Mixed Systems • Consider an open system where the number of moles (n) can change • dU = (U/V)dV + (U/S)dS + S(U/nj)dnj

  14. Chemical Potential • We can simplify with • and rewrite the dU equation as: dU = -PdV + TdS + Smjdnj • The third term is the chemical potential or:

  15. The Gibbs Function • Other characteristic functions can be written in a similar form • Gibbs function • For phase transitions with no change in P or T:

  16. Mass Flow • Consider a divided chamber (sections 1 and 2) where a substance diffuses across a barrier dS = dU/T -(m/T)dn dS = dU1/T1 -(m1/T1)dn1 + dU2/T2 -(m2/T2)dn2

  17. Conservation • Sum of dn’s must be zero: • Sum of internal energies must be zero: • Substituting into the above dS equation: dS = [(1/T1)-(1/T2)]dU1 - [(m1/T1)-(m2/T2)]dn1

  18. Equilibrium • Consider the equilibrium case (m1/T1) = (m2/T2) • Chemical potentials are equal in equilibrium

More Related