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Pure Substances

Pure Substances. Physics 313 Professor Lee Carkner Lecture 18. Exercise #17 Isenthalpic. For the initial state P i = 5 MPa, T i = 115 K Extrapolating we get: s 1 = 4.9945 kJ/ K kg and h 1 = 232.3 kJ/kg Isenthalpic process so s f = s i For s f =4.9945 and P f = 1 MPa, what is h f ?

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Pure Substances

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  1. Pure Substances Physics 313 Professor Lee Carkner Lecture 18

  2. Exercise #17 Isenthalpic • For the initial state • Pi = 5 MPa, Ti = 115 K • Extrapolating we get: • s1 = 4.9945 kJ/ K kg and h1 = 232.3 kJ/kg • Isenthalpic process so sf = si • For sf =4.9945 and Pf = 1 MPa, what is hf? • s(1 MPa and 110 K) = 4.875, s(1 MPa and 120 K) = • hf = 222.8 • P = mh = mDh = (118.2)(232.3-222.8) = • Annual energy form turbine = (1123 kW)(8769 hr/year) = 9.84X106 kWh • (9.84X106 kWh) ($0.075 per kWh) =

  3. Brian Greene to Speak Next Week • Author and host of “The Elegant Universe” • Expert on String Theory • A “theory of everything” • Monday May 3, 7:00pm, Olin Auditorium • “Breakthrough: Challenging What We Know” • Tuesday, May 4, 10:30am, 102 Science • Informal discussion with students and faculty • Go to one or the other and sign in, get 3 points extra credit on final exam

  4. Substances • A pure substance is either: • A homogenous mixture of several elements • PV and PT diagrams produce curves separating phases • PVT diagrams have surfaces as boundaries

  5. PV Diagram • The phase of a substance depends on its position on the PV diagram • Each point on the PV diagram represents:

  6. Saturation • The substance has to be at the saturation temperature for the pressure (or visa versa) in order to change phase

  7. Critical Point • Where the saturation curves intersect is the critical point • At temperatures higher than this there is no distinction between liquid and gas • Above the critical isotherm, no amount of pressure can condense the vapor to a liquid

  8. Steam Tables • PV and PT diagrams contain important information about substances • We often want specific information, but there may be no equation available and we don’t want to read off a graph • Sometimes called steam tables • Have to extrapolate between values

  9. PT Diagram • Three curves can be drawn on the PT diagram • Fusion curve • Vaporization curve • Sublimation curve • The curves bound three distinct regions, one for each phase • Juncture of the three curves is the triple point where all three coexist

  10. Other PT Features • An isobar at standard atmospheric pressure intersects the normal boiling and melting points • The critical point is on the vaporization curve • Gas above critical T is called “gas”, below it is called “vapor”

  11. Triple Points • Different solid phases are possible • Called polymorphs • Triple point is a point where any three phases coexist • The triple point is a triple line on a PV diagram

  12. PVT Diagram • Surfaces define volume regions where phases are allowed • Have a series of PT diagrams, one for each volume

  13. Types of PVT Curves • Substance does not change much with volume • Volume increase indicates density decrease • 4He has two different liquid phases and two triple points for a given volume

  14. Equations of State • The ideal gas law holds for low pressures

  15. Finding Critical Point • What defines the critical point? (P/ V) = 0 (2P/V2) = 0 • These two equations plus the equation of state itself gives you three equation and three unknowns • Substitute TC, PC, VC for T, P and V and solve

  16. Molar Heat Capacity • Heat capacity at constant pressure can be found by heating a sample at a uniform rate at constant pressure • Consider molar heat capacity • cP is zero at absolute zero and rises with T

  17. Debye Temperature • For 1 mol of a solid a certain number of atoms will be vibrating in the crystal lattice • Called the Debye temperature • cP falls rapidly below Debye temperature

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