1 / 96

Clausius-Clapeyron Equation

Clausius-Clapeyron Equation. And you thought you were already saturated!. Reading. Hess pp 39 - 42 pp 46 – 51 Tsonis pp 73 - 86 Wallace & Hobbs pp 97 – 99 Bohren & Albrecht pp 192-195, 202-203. Objectives.

apyle
Download Presentation

Clausius-Clapeyron Equation

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. Clausius-Clapeyron Equation And you thought you were already saturated!

  2. Reading • Hess • pp 39 - 42 • pp 46 – 51 • Tsonis • pp 73 - 86 • Wallace & Hobbs • pp 97 – 99 • Bohren & Albrecht • pp 192-195, 202-203

  3. Objectives • Be able to describe the physical processes of net evaporation, net condensation and equilibrium • Be able to describe the changes that occur to water substance as pressure and volume changes on a phase diagram

  4. Objective • Be able to state the only factor that determines the rate of evaporation from a water surface • Be able to state the factor that determines the rate of condensation of water molecules from the air

  5. Objective • Be able to determine if net evaporation, net condensation or equilibrium exists given a temperature and pressure on a pressure vs. temperature diagram for water substance

  6. Objective • Be able to perform calculations using the Clausius Clapyeron Equation, including the determination of saturation vapor pressure. • Be able to describe the change in boiling point temperature with pressure

  7. Objective • Be able to provide the definition of dew point and frost point from memory • Be able to provide the definition of relative humidity from memory

  8. Objective • Be able to calculate relative humidity • Be able to distinguish the difference between WMO and traditional defintions of relative humidity

  9. Twater Water at Equilibrium • Rate of evaporation • Constant • Function of water temperature

  10. Water at Equilibrium • Rate of Condensation • Variable • Function of water vapor mass in air

  11. Rate of evaporation Rate of condensation = Water at Equilibrium • At Equilibrium

  12. Water at Equilibrium • At Equilibrium • Rate of evaporation is a function of temperature Evaporation = f(T) Twater Rate of evaporation Rate of condensation =

  13. Tair Twater Rate of evaporation Rate of condensation = Water at Equilibrium • At Equilibrium • Rate of condensation also a function of temperature. Condensation = f(T)

  14. Tair Twater Rate of evaporation Rate of condensation = Water at Equilibrium • At Equilibrium Tair = Twater

  15. Water at Equilibrium • Water Vapor Partial Pressure • Function of mass of water vapor

  16. Water at Equilibrium • Equilibrium Curve Rate of Condendation = Rate of Evaporation es Equilibrium es = water vapor pressure at equilibrium (saturation) Pressure Temperature

  17. Condensation • Water Vapor Pressure > Equilibrium es e > es e Pressure Temperature

  18. Condensation • Water Vapor Pressure > Equilibrium Net Condensation es e > es e Pressure Temperature

  19. Condensation • Water Vapor Pressure > Equilibrium Condensation = Evaporation es e = es Pressure e Temperature

  20. e Evaporation • Water Vapor Pressure < Equilibrium es Net Evaporation Pressure e < es Temperature

  21. e Evaporation • Water Vapor Pressure < Equilibrium es Net Evaporation Pressure e < es Temperature

  22. Evaporation • Water Vapor Pressure < Equilibrium Condensation = Evaporation es e = es Pressure e Temperature

  23. Water at Equilibrium • Equilibrium Curve • Values es 1013 mb Pressure 6 mb 0oC 100oC Temperature

  24. Water at Equilibrium • Equilibrium Curve • Where do these numbers come from? es 1013 mb Pressure 6 mb 0oC 100oC Temperature

  25. Water at Equilibrium • Equilibrium Curve • Where do these numbers come from? Clausius-Clapeyron Equation Jaimie Clapeyron Thelma Clausius Famous Clip Art Scientists!

  26. Clausius-Clapeyron Equation Rudolf Clausius 1822 – 1888 German Mathematical Physicist Emile Clapeyron 1799 - 1864 French Engineer

  27. Clausius-Clapeyron Equation • The amount of moisture in the air (at equilibrium) depends on • Temperature of Air/Water • Water Vapor Pressure of Air • Volume (or Specific Volume) of Air Equilibrium es Pressure Constant Volume Temperature P-T Diagram

  28. Equilibrium es Constant Volume Pressure P-T Diagram Temperature Clausius-Clapeyron Equation • Our discussion assumed constant volume

  29. Clausius-Clapeyron Equation • The volume of water substance changes during phase changes Gas Solid Liquid

  30. Clausius-Clapeyron Equation • Pressure-Volume Diagram • Ideal Gas Pressure Volume

  31. Clausius-Clapeyron Equation • Pressure-Volume Diagram • Ideal Gas Pressure Volume

  32. Clausius-Clapeyron Equation • Pressure-Volume Diagram Vapor Water T3 O2 … -119oC N2 … -147oC H20 .. 347oC Pressure (e) Water & Vapor Vapor T2 T1 Volume (V)

  33. Pressure-Volume Diagram • Also known as Phase Diagram Water Vapor Pressure (e) Water & Vapor T2 T1 Volume (V)

  34. Pressure-Volume Diagram • Isotherms • T2>T1 Water Vapor Pressure (e) Water & Vapor T2 T1 Volume (V)

  35. Pressure-Volume Diagram • Vapor Phase • Ideal Gas Law • Decrease Volume • Increase Pressure Water Vapor Pressure (e) Water & Vapor T2 B T1 A Volume (V)

  36. Pressure-Volume Diagram • Water & Vapor Phase (B) • Slight Change in Volume Causes Condensation Water Vapor Pressure (e) Water & Vapor T2 B T1 Volume (V)

  37. Pressure-Volume Diagram • Water & Vapor Phase (B to C) • Condensation • Volume Decreasing • Constant Pressure at Constant Temp. Water Vapor Pressure (e) Water & Vapor T2 C B T1 Volume (V) Condensation

  38. Pressure-Volume Diagram • Water & Vapor Phase (B to C) • Condensation • Water Vapor Pressure is at Equilibrium (es) Water Vapor Pressure (e) Water & Vapor T2 C B T1 Volume (V)

  39. Pressure-Volume Diagram • Water Phase (C) • All Water Vapor Has Condensed Water Vapor Pressure (e) Water & Vapor T2 C T1 Volume (V)

  40. Pressure-Volume Diagram • Water Phase (C to D) • Volume Decreases Little • Virtually Incompressible D Water Vapor Pressure (e) Water & Vapor T2 C T1 Volume (V)

  41. Clausius-Clapeyron Equation • We’ve also ignored the heat required for phase change + =

  42. Water Vapor Pressure (e) Water & Vapor T2 T1 Volume (V) Clausius-Clapeyron Equation • Let’s investigate all these variables using the Carnot Cycle!

  43. Clausius-Clapeyron Equation • Reversible cycle C B Water Vapor Pressure (e) Water & Vapor T2 D A T1 Specific Volume (a)

  44. Clausius-Clapeyron Equation • At Point A Water Vapor es = Pressure T1 = Temperature aw = Volume C B Water & Vapor T2 Pressure (e) A D es T1 es,T1 , aw Specific Volume (a)

  45. Clausius-Clapeyron Equation • At Point B es+Des T1+DT aw +Daw Water Vapor Vapor Pressure es+Des Temperature T2 = T1+DT Volume aw +Daw es +Des C B Water & Vapor T2 Pressure (e) A D es T1 es,T1 , aw Specific Volume (a)

  46. Clausius-Clapeyron Equation • At Point C es+Des T1+DT av +Dav Water Vapor Pressure es+Des Temperature T2 = T1+DT Volume av +Dav es +Des C Vapor B Water & Vapor T2 Pressure (e) A D es T1 es,T1 , av Specific Volume (a)

  47. Clausius-Clapeyron Equation • At Point D es+Des T1+DT av +Dav Water Vapor es = Pressure T1 = Temperature av = Volume es +Des C Vapor B Water & Vapor T2 Pressure (e) A D es T1 es,T1 , av Specific Volume (a)

  48. Clausius-Clapeyron Equation • First Law of Thermodynamics • Second Law of Thermodynamics

  49. Clausius-Clapeyron Equation • Combine the equations • Integrate over the closed path

  50. Clausius-Clapeyron Equation • For a cyclic process • So …..

More Related