A&OS C110/C227: Review of thermodynamics and dynamics I Robert Fovell UCLA Atmospheric and Oceanic Sciences 1

Notes Everything in this presentation should be familiar Please feel free to ask questions, and remember to refer to slide numbers if/when possible If you have Facebook, please look for the group “UCLA_Synoptic”. You need my permission to join. (There are two “Robert Fovell” pages on FB. One is NOT me, even though my picture is being used.) 2

Elementary stuff 3

The atmosphere Primordial atmosphere Volcanic activity, rock outgassing H 2 O vapor, CO 2, N 2, S… no oxygen Origin of oxygen: dissociation of water vapor by absorption of UV (minor), and photosynthesis (major) Present composition of dry air 78% N 2 21% O 2 1% Ar “Minor” constituents of dry air include CO %, CH %, O 3 < % 4

Time series of CO 2 5

Atmosphere: Dry and moist Dry air constituents are well-mixed and vary only slowly over time and space Roughly constant over lowest 80 km (50 mi) Very convenient for thermodynamic calculations Water vapor (“wv”) 0-4% of total atmospheric mass, but also concentrated near surface for these reasons Surface source Efficient return mechanism (precipitation) Absolute humidity is a very strong function of temperature (T) Revealed by Clausius-Clapeyron equation 6

Standard atmosphere Averaged over time and horizontal space Four layers: Troposphere Stratosphere Mesosphere Thermosphere “Lapse rate” = how T decreases with height Temperature vs. height for standard atmosphere 7

Standard atmosphere Troposphere “turning sphere” Averages 12 km (7.5 mi) deep Top = tropopause T range sfc to - 60˚C at tropopause Average tropospheric lapse rate: 6.5˚C/km (19˚F/mi) Temperature vs. height for standard atmosphere 8

Standard atmosphere Stratosphere “layered”… very stable Extends upward to 50 km Top = stratopause T increases with height (lapse rate negative) UV interception by O 2 and O 3 “lid” for troposphere… in a sense Temperature vs. height for standard atmosphere 9

Standard atmosphere Mesosphere “middle sphere” T decreases with height again Top = mesopause Thermosphere Very hot… and yet no “heat” (very little mass) Freeze and fry simultaneously Temperature vs. height for standard atmosphere 10

Standard atmosphere Tropospheric T variation 15˚C at surface -60˚C at 12 km elevation If “warm air rises and cold air sinks”, why doesn’t the troposphere turn over? Temperature vs. height for standard atmosphere 11

Pressure Pressure = force per unit area p = N/m 2 = Pascal (Pa) Air pressure largely due to weight of overlying air Largest at the surface, zero at atmosphere top Decreases monotonically with height (z) Pressure linearly proportional to mass 12

Pressure 13 g ~ 9.81 m/s 2 at sea-level

Sea-level pressure (SLP) mb = millibar hPa = hectopascal 1 mb = 100 Pa 14 For surface p = 1000 mb: 50% of mass below 500 mb 80% of mass below 200 mb 99.9% of mass below 1 mb

Various p and z levels 15 Infer how pressure varies with height

Pressure vs. height 16 P 0 = reference (surface) pressure H = scale height

Density =  = mass/volume 17 Infer how density varies with height

p and  vs. height 18 and  and ln 

Warm air rises and cold air sinks… NOT always true. True statement is: less dense air rises, more dense air sinks Note near-surface air, although warm, is also more dense Temperature vs. height for standard atmosphere 19

Warm air rises and cold air sinks… Temperature vs. height for standard atmosphere 20

Basic thermodynamics concepts 21

System and environment System = what we wish to study View as control mass or control volume Control mass (CM) Define some mass, hold fixed, follow it around Control volume (CV) Define and monitor a physical space Environment = everything else that may interact with the system 22

System states Systems may be open or closed to mass Open systems permit mass exchange across system boundaries Our CVs are usually open Strictly speaking, a CM is closed Closed systems may be isolated or nonisolated Isolated systems do not permit energy transfer with environment Closed, isolated system = environment doesn’t matter 23

Lagrangian vs. Eulerian CM is the Lagrangian viewpoint Powerful, desirable but often impractical Total derivatives Freeway example CV is the Eulerian viewpoint Observe flow through volume Partial derivatives 24

Air parcel Our most frequently used system CM (usually!) – Lagrangian concept Monitor how T, p, and V change as we follow it around 25

Conventions We often use CAPITAL letters for extensive quantities, and lower case for specific quantities Specific = per unit mass Example: U is internal energy, in Joules u is specific internal energy, in J/kg Unfortunately, “u” is also zonal wind velocity Aside: Temperature T is essentially specific, but capitalized (and isn’t per unit mass anyway) Pressure p is fundamentally extensive, but lower case (and isn’t per unit mass anyway) 26

Energy and the 1 st law Total energy = KE + PE + IE Conserved in absence of sources and sinks Our main use of 1 st law: monitor changes in internal energy (IE or u) owing to sources and sinks How do we change system u? With energy transfer via heat Q or q work W or w Caveat: w is also vertical velocity, and q may also refer to water vapor specific humidity 27

Work Work = force applied over a distance Force: N, distance: m Work: Nm = J = energy Our principal interest: CM volume compression or expansion (dV) in presence of external pressure (p) W > 0 if dV > 0 28

Work 29 W > 0 when system expands against environment

Heat Diabatic heat Diabatic: Greek for “passable, to be passed through” Internal energy exchanged between system and environment q > 0 when energy flow is INTO system Adiabatic = system is isolated Adiabatic: Greek for “impassable, not to be passed through” 30

Caution on nomenclature We should use diabatic when the energy exchange is between system and environment But, what if the heat source or sink is inside the system? That’s adiabatic, but q ≠ 0 Our interior heat source will be water changing phase Dry adiabatic: q = 0 No heat source, outside OR inside “dry” really means no water phase changes Moist adiabatic: q ≠ 0, but heat source/sink is inside system “moist” implies water phase change Synonyms include “saturated adiabatic” and “wet adiabatic” Can also be referred to as “diabatic”! 31

1 st law and Carnot cycle 32

1 st law In the absence of ∆KE and ∆PE Other ways of writing this 33 Most of my examples will be per unit mass.

State properties Internal energy u is a state property Changes in state properties are not path-dependent Other state properties include m, T, p, , V, etc. 34

State properties 35

Path-dependence Work and heat are path-dependent 36

Path-dependence A cyclic process starts and ends with the same state property values … but the cyclic process can have net heat exchange and do net work 37

Path-dependence 38 Black path

Path-dependence 39 Red path

Carnot cycle 4-step piston cycle on a CM 2 steps of volume expansion, 2 of volume compression 2 steps are isothermal, 2 are (dry) adiabatic Warm and cold thermal reservoirs external to system Start and end with temperature T 1 and volume V 1 40

Carnot – Step 1 41 Isothermal volume expansion Add heat Q A from warm reservoir T 2 = T 1 V 2 > V 1

Carnot – Step 2 42 Adiabatic volume expansion No heat exchange T 3 < T 2 V 3 > V 2

Carnot – Step 3 43 Isothermal volume compression Lose heat Q B to cold thermal reservoir T 4 = T 3 V 4 < V 3

Carnot – Step 4 44 Adiabatic volume compression No heat exchange T 1 > T 4 V 1 < V 4 Returned to original state T 1, V 1. Cycle is complete.

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Apply 1 st law 46

Carnot on T-V diagram 47

Carnot on T-V diagram 48

Carnot on T-V diagram 49

Carnot on T-V diagram 50

Carnot on T-V diagram 51

Carnot on T-V diagram 52

Carnot on T-V diagram 53 No net ∆V But did net W

Conceptual summary 54 Heat flow diverted to do work

Question for thought #1 55 The isothermal expansion (Q A ) occurred at a higher temperature than the Isothermal compression (Q B ). What does this imply for the work? What does this imply for the pressure? Q B is waste heat. What does this imply for the efficiency of this heat engine? Is there a limit to efficiency? Is the limit found in the 1 st law?

Question for thought #2 56 Can you design a cyclic process that does no net work? What would it look like on a T-V diagram?

Useful forms of the 1 st law 57 for ideal gases only (where h = enthalpy) these can be used to create these useful forms (  = 1/  = specific volume) we can also write this in terms of potential temperature for dry air, c p = 1004 J/(kg K), and c v = 717 J/(kg K)

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