A&OS C110/C227: Review of thermodynamics and dynamics IRobert FovellUCLA Atmospheric and Oceanic Sciencesrfovell@ucla.edu

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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.)

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Elementary stuff

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The atmosphere• Primordial atmosphere• Volcanic activity, rock outgassing• H2O vapor, CO2, N2, S… no oxygen

• Origin of oxygen: dissociation of water vapor by absorption of UV (minor), and photosynthesis (major)

• Present composition of dry air• 78% N2

• 21% O2

• 1% Ar• “Minor” constituents of dry air include• CO2 0.039%, CH4 0.00018%, O3 < 0.00005%

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Time series of CO2

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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

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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

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Standard atmosphere• Troposphere• “turning sphere”• Averages 12 km (7.5

mi) deep• Top = tropopause• T range 15˚C @ sfc to -

60˚C at tropopause• Average tropospheric

lapse rate: 6.5˚C/km (19˚F/mi)

Temperature vs. height for standard atmosphere

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Standard atmosphere• Stratosphere• “layered”… very stable• Extends upward to 50

km• Top = stratopause• T increases with height

(lapse rate negative)• UV interception by O2

and O3

• “lid” for troposphere… in a sense

Temperature vs. height for standard atmosphere

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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

simultaneouslyTemperature vs. height for standard atmosphere

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Standard atmosphere• Tropospheric T

variation15˚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

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Pressure• Pressure = force per unit area

p = N/m2 = 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

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Pressure

13g ~ 9.81 m/s2 at sea-level

Sea-level pressure (SLP)

mb = millibarhPa = hectopascal1 mb = 100 Pa

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For surface p = 1000 mb:50% of mass below 500 mb80% of mass below 200 mb99.9% of mass below 1 mb

Various p and z levels

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Infer how pressure varies with height

Pressure vs. height

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P0 = reference (surface) pressureH = scale height

Density = r = mass/volume

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Infer how density varies with height

p and r vs. height

18and r and ln r

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

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Warm air rises and cold air sinks…

Temperature vs. height for standard atmosphere

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Basic thermodynamics concepts

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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

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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

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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

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

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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 1st law• Total energy = KE + PE + IE• Conserved in absence of sources and sinks

• Our main use of 1st 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

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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

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Work

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W > 0 when system expands againstenvironment

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”

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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

1st law and Carnot cycle

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1st law• In the absence of ∆KE and ∆PE

• Other ways of writing this

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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, r, V, etc.

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State properties

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Path-dependence• Work and heat are path-dependent

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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

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Path-dependence

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Black path

Path-dependence

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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 T1 and volume V1

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Carnot – Step 1

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Isothermal volume expansion

Add heat QA from warmreservoir

T2 = T1

V2 > V1

Carnot – Step 2

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Adiabatic volume expansion

No heat exchange

T3 < T2

V3 > V2

Carnot – Step 3

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Isothermal volume compression

Lose heat QB to cold thermalreservoir

T4 = T3

V4 < V3

Carnot – Step 4

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Adiabatic volume compression

No heat exchange

T1 > T4

V1 < V4

Returned to original state T1, V1.Cycle is complete.

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Apply 1st law

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Carnot on T-V diagram

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Carnot on T-V diagram

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Carnot on T-V diagram

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Carnot on T-V diagram

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Carnot on T-V diagram

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Carnot on T-V diagram

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Carnot on T-V diagram

53No net ∆V

But did net W

Conceptual summary

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Heat flow divertedto do work

Question for thought #1

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The isothermal expansion (QA) occurred at a higher temperature than the Isothermal compression (QB).

What does this imply for the work?What does this imply for the pressure?

QB 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 1st law?

Question for thought #2

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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 1st law

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• for ideal gases only (where h = enthalpy)

• these can be used to create these useful forms (a = 1/r = specific volume)

• we can also write this in terms of potential temperature

• for dry air, cp = 1004 J/(kg K), and cv = 717 J/(kg K)

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