1. Pure Substances Physics 313 Professor Lee Carkner Lecture 18

2. 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 ?  s(1 MPa and 110 K) = 4.875, s(1 MPa and 120 K) =  h f = 222.8  P = mh = m  h = (118.2)(232.3-222.8) =  Annual energy form turbine = (1123 kW)(8769 hr/year) = 9.84X10 6 kWh  (9.84X10 6 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:  

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

8. 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

10. 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

11. 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

13. 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” 

14. 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

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

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

20. Equations of State   The ideal gas law holds for low pressures 

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

22. 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   c P is zero at absolute zero and rises with T

24. Debye Temperature  For 1 mol of a solid a certain number of atoms will be vibrating in the crystal lattice   Called the Debye temperature  c P falls rapidly below Debye temperature 