Lecture 8

1. Lecture 8 Saturated Adiabatic Processes

2. Liquid Phase Changes condensation Gas (Vapor) evaporation melting deposition sublimation freezing Solid (Ice) Energy absorbed Energy released

3. Latent Heat • Heat released or absorbed during a phase change of water • AMS Glossary

4. Latent Heats at 0C • Latent heats of vaporization (evaporation) and condensation (Lv): ~ 600 calg-1 • Latent heats of fusion (freezing) and melting (Lf): ~ 80 calg-1 • Latent heats of sublimation and deposition (Ls): ~ 680 calg-1 • Conversion: 1 calg-1 = 4.1855 x 103 Jkg-1

5. Exercise • Convert Lv to Jkg-1 • Lv = (600 calg-1) x 4.1855x 103Jkg-1 = 2.5 x 106 Jkg-1

6. Exercise • Suppose that the mixing ratio (w) of a parcel is 2.0 x 10-2 • (20g water vapor per kg of dry air) • Suppose that 10% of the vapor condenses • How much does the parcel warm? • (Assume constant pressure.)

7. Solution, Part 1 • Q = -Lvmv, where mv is the mass of water vapor • (Why the negative sign?) • q  -Lv w = - (2.5 x 106 Jkg-1)(-2.0 x 10-3) = 5.0 x 103 Jkg-1

8. Solution, Part 2 • Temperature change at constant pressure: But, cp 1000 Jkg-1 kg-1 

9. A Saturated Adiabatic System • Consider a parcel consisting of dry air, water vapor, and liquid water • Closed system, saturated • Consider adiabatic transitions • i.e., no heat enters or leaves system

10. Saturated Adiabatic Transitions • Expansion  cooling  condensation • i.e., water vapor decreases, liquid water increases • Condensational heating partially offsets cooling due to expansion • Result: Cooling rate less than dry adiabatic rate • Compression  warming  evaporation • i.e., water vapor increases, liquid water decreases • Evaporative cooling partially offsets heating due to compression • Result: Heating rate less than dry adiabatic rate

11. Comparison Unsaturated parcel Saturated parcel z Temperature

12. Dry and Saturated Adiabats Dry Saturated Pressure Temperature

13. Temperature of Lifted Parcel • Consider a parcel that is initially unsaturated • Parcel is lifted to LCL and beyond

14. z LCL Temperature

15. z LCL Temperature

16. z LCL Temperature

17. z LCL Temperature

18. z LCL Temperature

19. z LCL Temperature

20. z LCL Temperature

21. z LCL Temperature

22. z LCL Temperature

23. z LCL Temperature

24. z LCL Temperature

25. z LCL Temperature

26. z LCL Temperature

27. z LCL Temperature

28. Wet-Bulb Temperature, Tw The wet-bulb temperature is the temperature associated with a wick-covered thermometer on a psychrometer.

29. Measuring Humidity: Sling psychrometer A psychrometer consists of two glass thermometers with one covered with a wick (cloth) that is wet. This measures the ‘wet-bulb’ temperature.

30. Physical Basis of Tw Evaporation will occur on a wick at a steady rate (as sling is slung). Heat must be continually supplied in an amount = the latent heat of vaporization of the water. Heat is taken from the air passing over the wick of the thermometer – resulting in a drop in temperature!

31. Physical Basis of Tw If air is saturated, no evaporation takes place. Temperature of the wet bulb is same as dry bulb. If air is very dry, the wet-bulb depression may be substantial. Wet-bulb depressionis the T-Tw

32. Dew Point vs. Wet Bulb Temperature Dew point is when we cool a volume of air until saturation is reached while keeping moisture content constant. Wet-bulb temperature we obtain if we cool air to saturation by evaporating water into it. Therefore, saturation is reached at a higher temperature than dew point. Td≤ Tw ≤ T

33. Normand’s Rule States that the wet-bulb temperature may be determined by lifting a parcel of air adiabatically to its LCL and then following a moist adiabat from that temperature back down to the parcel’s actual temperature.

34. Relationship between dew point, wet-bulb and dry bulb temperatures