at620 review for midterm #1 part 1: chapters 1-4 brenda dolan october 17, 2005 part 1: chapters 1-4...
Post on 21-Dec-2015
218 views
TRANSCRIPT
AT620 Review for Midterm #1
AT620 Review for Midterm #1
Part 1: Chapters 1-4Brenda Dolan
October 17, 2005
Part 1: Chapters 1-4Brenda Dolan
October 17, 2005
Exam: 21 October 2005Exam: 21 October 2005
Exam is closed book You may bring a calculator You will have 2 hours to complete the exam (8-10am)
Bring your own paper
Exam is closed book You may bring a calculator You will have 2 hours to complete the exam (8-10am)
Bring your own paper
Chapter 1 Overview of Cloud Dynamics
Chapter 1 Overview of Cloud Dynamics
Chapter 1: Overview of Cloud Dynamics
Chapter 1: Overview of Cloud Dynamics
Cloud Dynamics: The study of the evolution of clouds including their formation and dissipation mechanisms, cloud air motions and the forces creating those motions. Cloud dynamics is a macroscopic view of clouds from an ensemble perspective.
Cloud Microphysics: the detailed examination of individual cloud particle physics. This is more a microscopic understanding of clouds.
Convective Clouds: “Wet chemical reactors”—transforming particles and gases into acid precipitation. Important vertical transport of heat, moisture, gases, aerosols and momentum from the Earth’s surface to the low, middle, and upper troposphere, and even the lower stratosphere.
Cloud Dynamics: The study of the evolution of clouds including their formation and dissipation mechanisms, cloud air motions and the forces creating those motions. Cloud dynamics is a macroscopic view of clouds from an ensemble perspective.
Cloud Microphysics: the detailed examination of individual cloud particle physics. This is more a microscopic understanding of clouds.
Convective Clouds: “Wet chemical reactors”—transforming particles and gases into acid precipitation. Important vertical transport of heat, moisture, gases, aerosols and momentum from the Earth’s surface to the low, middle, and upper troposphere, and even the lower stratosphere.
Chapter 1: Overview of Cloud Dynamics
Chapter 1: Overview of Cloud Dynamics
Layer Clouds: Important radiative properties for climate and the global heat budget. Much larger coverage.
Cumulus clouds: primarily buoyancy-driven clouds. An ascending parcel cools adiabatically, increasing the relative humidity, and once the RH is ~100%, hygroscopic aerosol particles take on water vapor and form cloud droplets.
Lagrangian time scale (Tp): the time it takes a parcel of air to enter the base of a cloud and exit the top.
Total lifetime of the cloud (TL)
Layer Clouds: Important radiative properties for climate and the global heat budget. Much larger coverage.
Cumulus clouds: primarily buoyancy-driven clouds. An ascending parcel cools adiabatically, increasing the relative humidity, and once the RH is ~100%, hygroscopic aerosol particles take on water vapor and form cloud droplets.
Lagrangian time scale (Tp): the time it takes a parcel of air to enter the base of a cloud and exit the top.
Total lifetime of the cloud (TL)
Chapter 1: Overview of Cloud Dynamics
Chapter 1: Overview of Cloud Dynamics
Cloud Type H(m) W(m/s) Tp LWC g/m3
Comments
Ordinary cumulus
1500 3 10 min 0.5-1 ABL, shallow
Towering cumulus
5000 10 10 min 1.0-1.5 Larger than Ordinary Cu, more LWMore unstable air, weaker capping inversion, convergence0
Cumulonimbus 10,000 15 10 min 2.5-4 Grow in very unstable conditions
Supercell 12,000 40 5 min Can last 2-6 hours; characteristic BWER
Fog 100 0.01 3 hr .10 Radiation, frontal, advection, ice/snow
Stratocumulus 1000 0.1 3 hr 0.05-0.25 BL clouds driven by radiative cooling at top
Stable Orographic clouds
Variable 15 20 min < 1.0 Air just ascends with topography
Chapter 2 Basic Thermodynamics
Chapter 2 Basic Thermodynamics
Chapter 2: Basic ThermodynamicsChapter 2: Basic Thermodynamics
Isothermal Process: A change in state occurring at constant temperature.
Adiabatic Process: A change in state occurring without the transfer of thermal energy between the system and its surroundings.
Cyclic Process: A change occurring when the system (although not necessarily its surroundings) is returned to its initial state.
Isothermal Process: A change in state occurring at constant temperature.
Adiabatic Process: A change in state occurring without the transfer of thermal energy between the system and its surroundings.
Cyclic Process: A change occurring when the system (although not necessarily its surroundings) is returned to its initial state.
Chapter 2: Basic ThermodynamicsChapter 2: Basic Thermodynamics
Equation of State: Ideal gas law (For a unit mass) (For molecules)
Other relations n=m/M R=R*/M k=R*/NA
Rd=287 J K-1 kg-1 (Dry gas constant) Rv=461 J K-1 kg-1 (Water vapor gas constant)
Equation of State: Ideal gas law (For a unit mass) (For molecules)
Other relations n=m/M R=R*/M k=R*/NA
Rd=287 J K-1 kg-1 (Dry gas constant) Rv=461 J K-1 kg-1 (Water vapor gas constant)
pV =mRTp =ρRT
pV =nR* Tp =RT / α
p =n0kT
Chapter 2: Basic ThermodynamicsChapter 2: Basic Thermodynamics
First Law of Thermodynamics Conservation of energy: The amount of internal energy
in a system is equal to the heat added to the system minus the work done by the system. dq=du+dw dq=du+pdα dq=CvdT+pdα dq=CpdT-αdp dq=dh-αdp (In terms of enthalpy) Tds=du+pdα (In terms of entropy)
“PV Work” dw=pdV
First Law of Thermodynamics Conservation of energy: The amount of internal energy
in a system is equal to the heat added to the system minus the work done by the system. dq=du+dw dq=du+pdα dq=CvdT+pdα dq=CpdT-αdp dq=dh-αdp (In terms of enthalpy) Tds=du+pdα (In terms of entropy)
“PV Work” dw=pdV
w = pdV =nR* Td(lnV)v1
v2
∫v1
v2
∫
Chapter 2: Basic ThermodynamicsChapter 2: Basic Thermodynamics
Internal energy du=dq-dw du=dw (Adiabatic process) du=cvdT (specific internal energy) Joule’s law: Internal energy of an ideal gas is a function of
temperature only. (this comes from the fact that ideal gas molecules are not attracted to one another)
Enthalpy The amount of energy in a system capable of doing
mechanical work. h=u+pα dh=αdp dh=cpdT (For constant p or adiabatic process)
Internal energy du=dq-dw du=dw (Adiabatic process) du=cvdT (specific internal energy) Joule’s law: Internal energy of an ideal gas is a function of
temperature only. (this comes from the fact that ideal gas molecules are not attracted to one another)
Enthalpy The amount of energy in a system capable of doing
mechanical work. h=u+pα dh=αdp dh=cpdT (For constant p or adiabatic process)
Chapter 2: Basic ThermodynamicsChapter 2: Basic Thermodynamics
• 2nd Law of Thermodynamics: 1) Thermal energy flows from warmer to colder (thermal energy
will not spontaneously flow from a colder to a warmer object)
2) The entropy of the universe is constantly increasing
Entropy “The amount of disorder in a system”
(Reversible process)ds=0 for adiabatic processesThere is no change in entropy for a reversible process
• 2nd Law of Thermodynamics: 1) Thermal energy flows from warmer to colder (thermal energy
will not spontaneously flow from a colder to a warmer object)
2) The entropy of the universe is constantly increasing
Entropy “The amount of disorder in a system”
(Reversible process)ds=0 for adiabatic processesThere is no change in entropy for a reversible process
ds =dqT
Chapter 2: Basic ThermodynamicsChapter 2: Basic Thermodynamics
Carnot Cycle A series of state changes of working substance in which its
volume changes and it does external work Work done by Ttwo adiabatic and two isothermal legs
dw=-du=-cvdT (Adiabatic legs) pVϒ=const. dw=RTdα/α (Isothermal legs)
Initial and final states are the same du=0 for the system net heat absorbed=work done by working substance (dq=dw)
Efficiency (η):
Example: Hurricane
Carnot Cycle A series of state changes of working substance in which its
volume changes and it does external work Work done by Ttwo adiabatic and two isothermal legs
dw=-du=-cvdT (Adiabatic legs) pVϒ=const. dw=RTdα/α (Isothermal legs)
Initial and final states are the same du=0 for the system net heat absorbed=work done by working substance (dq=dw)
Efficiency (η):
Example: Hurricane
η =Qc − Qh
Qh
=work done
heat absorbed
η =Ts − Tp
Ts
Chapter 2: Basic ThermodynamicsChapter 2: Basic Thermodynamics
Carnot Cycle Carnot Cycle
Chapter 2: Basic ThermodynamicsChapter 2: Basic Thermodynamics Free Energy
Helmholz Free Energy (or Helmholz function) Sets upper limit on the amount of non-pV work possible at
constant T, V (it is free energy since its decrease represents the maximum energy that can be freed in a process and made available for work)
Transitions can only take place to a state with a lower free energy
Gibbs Free Energy (or Gibbs function) Sets upper limit on the amount of non-pV work possible at
constant T, P (it is free energy since its decrease represents the maximum energy that can be freed in a process and made available for work)
Transitions can only take place to a state with a lower free energy
Free Energy Helmholz Free Energy (or Helmholz function)
Sets upper limit on the amount of non-pV work possible at constant T, V (it is free energy since its decrease represents the maximum energy that can be freed in a process and made available for work)
Transitions can only take place to a state with a lower free energy
Gibbs Free Energy (or Gibbs function) Sets upper limit on the amount of non-pV work possible at
constant T, P (it is free energy since its decrease represents the maximum energy that can be freed in a process and made available for work)
Transitions can only take place to a state with a lower free energy
F =U −TSdF =−pdV −SdT
G =U −TSG =F + PV =U −TS+ PV
dG =Vdp−SdT
Chapter 2: Basic ThermodynamicsChapter 2: Basic Thermodynamics Free Energy
Spontaneous Processes: A process in which the system tends to equilibrium
∆F,G<0 (Spontaneous process) ∆F,G=0 (Equilibrium process) ∆F,G>0 (Forbidden process)
Chemical potential Change in internal energy per mole of substance when
material is added or taken away from the system
(Gibbs free energy)
Free Energy Spontaneous Processes:
A process in which the system tends to equilibrium ∆F,G<0 (Spontaneous process) ∆F,G=0 (Equilibrium process) ∆F,G>0 (Forbidden process)
Chemical potential Change in internal energy per mole of substance when
material is added or taken away from the system
(Gibbs free energy)
μ =δU
δn⎛⎝⎜
⎞⎠⎟
S ,V
μ =δG
δn⎛⎝⎜
⎞⎠⎟
T , p
Chapter 2: Basic ThermodynamicsChapter 2: Basic Thermodynamics Phase changes
For a system consisting of phases, to be in equilibrium it must be in thermal, mechanical, and chemical equilibrium: T1=T2=...=TΦ
p1=p2=...=pΦ
µ1=µ2=...=µΦ
Phase transition equilibrium gl=gv
∆g=0 For a substance in stable equilibrium between different phases,
the specific Gibbs energy of those phases are equal. Latent Heat
Amount of heat absorbed or given off (released) during a phase change
Phase changes For a system consisting of phases, to be in equilibrium it must
be in thermal, mechanical, and chemical equilibrium: T1=T2=...=TΦ
p1=p2=...=pΦ
µ1=µ2=...=µΦ
Phase transition equilibrium gl=gv
∆g=0 For a substance in stable equilibrium between different phases,
the specific Gibbs energy of those phases are equal. Latent Heat
Amount of heat absorbed or given off (released) during a phase change
dQ =L * m
sv −sl =Llv
T
Chapter 2: Basic ThermodynamicsChapter 2: Basic Thermodynamics Clausius-Clapeyron equation
Describes the variation in (vapor) pressure with temperature for a system consisting of two phases in equilibrium at a pressure and temperature.
AND, T,e are same, so equate and rearrange:
(Integrated form)
Clausius-Clapeyron equation Describes the variation in (vapor) pressure with
temperature for a system consisting of two phases in equilibrium at a pressure and temperature.
AND, T,e are same, so equate and rearrange:
(Integrated form)
dgl =−SldT +V ldedgv =−SvdT +Vvdedgv =dgl
de
dT=
Llv
T(Vv −V l )
ln e =−Llv
RT+ const.
Chapter 2: Basic ThermodynamicsChapter 2: Basic Thermodynamics Surface Tension, σ
Inward pull of molecules. It requires work to move a molecule from center to the outside (kind of like PE) Work must be done to create a curved surface (σdΩ) Treat interface as its own “phase”
Surface Tension, σ Inward pull of molecules. It requires work to move a
molecule from center to the outside (kind of like PE) Work must be done to create a curved surface (σdΩ) Treat interface as its own “phase”
Chapter 3 Nucleation of Liquid
Droplets
Chapter 3 Nucleation of Liquid
Droplets
Chapter 3: Nucleation of Liquid Droplets
Chapter 3: Nucleation of Liquid Droplets
Homogeneous (Spontaneous) Nucleation Random clustering of drops (chance aggregation of vapor
molecules) through thermal kinetic energy collisions Does not occur in the atmosphere because it requires very
high supersaturations (12%) Two forms of energy involved in process:
Bulk thermodynamic energy (volume)
Surface energy (Area)
Homogeneous (Spontaneous) Nucleation Random clustering of drops (chance aggregation of vapor
molecules) through thermal kinetic energy collisions Does not occur in the atmosphere because it requires very
high supersaturations (12%) Two forms of energy involved in process:
Bulk thermodynamic energy (volume)
Surface energy (Area)
BTE =nLV(μL −μv)
SE =Aσ LV
Chapter 3: Nucleation of Liquid Droplets
Chapter 3: Nucleation of Liquid Droplets
The total energy change associated with the spontaneous formation of a droplet of volume V and surface area A is:
(chemical potential)
(for spherical drop)
Critical radius R* (Kelvin’s Equation) The radius at which a drop is in unstable equilibrium. If it gains
one molecule, it will continue to grow. If one molecule leaves it will continue to evaporate.
The total energy change associated with the spontaneous formation of a droplet of volume V and surface area A is:
(chemical potential)
(for spherical drop)
Critical radius R* (Kelvin’s Equation) The radius at which a drop is in unstable equilibrium. If it gains
one molecule, it will continue to grow. If one molecule leaves it will continue to evaporate.
ΔG = −nLV (μ v − μ L ) + Aσ LV
ΔG = −nL
4
3π R3kT ln
e
es
⎛
⎝⎜⎞
⎠⎟+ 4π R2σ LV
R* =2σ LV
nLkT lnees
⎛
⎝⎜⎞
⎠⎟
Chapter 3: Nucleation of Liquid Droplets
Chapter 3: Nucleation of Liquid Droplets
Critical energy barrier The energy that must be overcome by fluctuations in
the system in order to produce a critically-sized embryo.
Critical energy barrier The energy that must be overcome by fluctuations in
the system in order to produce a critically-sized embryo.
ΔG* =16πσ LV
3
3 nLkT ln ees
( )⎡⎣⎢
⎤⎦⎥
2
1) e/es < 1 sub-saturated∆G>0 for all R
2) e/es > 1 super-saturated∆G + or –
Chapter 3: Nucleation of Liquid Droplets
Chapter 3: Nucleation of Liquid Droplets
Relative humidity (e/es) above a pure water droplet of a known radius:
Supersaturation S=(1-e/es)*100
Relative humidity (e/es) above a pure water droplet of a known radius:
Supersaturation S=(1-e/es)*100
e
es
=exp2σ LV
nLkTr⎡
⎣⎢
⎤
⎦⎥
Chapter 3: Nucleation of Liquid Droplets
Chapter 3: Nucleation of Liquid Droplets
Nucleation on Insoluble Particles (but wettable) Flat, insoluble surface
Φ, Contact angle between substrate surface and the tangent line to the droplet surface (wettable surface, Φ =0º, non-wettable surface Φ =180º)
Add a new term to dG Critical Radius:
Catalyst just increases the chance of random formation of a larger drop (R* does not change)
Critical energy barrier:
Where f(m)=(2+m)(1-m)2/4
Nucleation on Insoluble Particles (but wettable) Flat, insoluble surface
Φ, Contact angle between substrate surface and the tangent line to the droplet surface (wettable surface, Φ =0º, non-wettable surface Φ =180º)
Add a new term to dG Critical Radius:
Catalyst just increases the chance of random formation of a larger drop (R* does not change)
Critical energy barrier:
Where f(m)=(2+m)(1-m)2/4
R* =2σ LV
nLkT lnees
⎛
⎝⎜⎞
⎠⎟
ΔG* =16πσ LV
3
3 nLkT ln ees
( )⎡⎣⎢
⎤⎦⎥
2 f (m)
Chapter 3: Nucleation of Liquid Droplets
Chapter 3: Nucleation of Liquid Droplets
Nucleation on Insoluble Particles (but wettable) Curved, insoluble surface
Critical Radius:
Catalyst just increases the chance of random formation of a larger drop (R* does not change)
Critical energy barrier:
where f(m)=(2+m)(1-m)2/4 and x=r/r* (ratio of radii of dry particle radius to critical droplet radius
2 things play a role in determining saturation ratio: size of nucleating particle wettability
Nucleation on Insoluble Particles (but wettable) Curved, insoluble surface
Critical Radius:
Catalyst just increases the chance of random formation of a larger drop (R* does not change)
Critical energy barrier:
where f(m)=(2+m)(1-m)2/4 and x=r/r* (ratio of radii of dry particle radius to critical droplet radius
2 things play a role in determining saturation ratio: size of nucleating particle wettability
R* =2σ LV
nLkT lnees
⎛
⎝⎜⎞
⎠⎟
ΔG* =16πσ LV
3
3 nLkT ln ees
( )⎡⎣⎢
⎤⎦⎥
2 f (m, x)
Chapter 3: Nucleation of Liquid Droplets
Chapter 3: Nucleation of Liquid Droplets
Nucleation on water-soluble particles Raoult’s Law
The vapor pressure of component A above the solution is less than the vapor pressure of component A in pure form by the factor
The presence of a solute B (e.g. salt) lowers the energy barrier associated with nucleation
Saturation ratio for a solution drop: curvature + solution terms
Nucleation on water-soluble particles Raoult’s Law
The vapor pressure of component A above the solution is less than the vapor pressure of component A in pure form by the factor
The presence of a solute B (e.g. salt) lowers the energy barrier associated with nucleation
Saturation ratio for a solution drop: curvature + solution terms
eA =nA
nA +nB
eAO
e
es
=exp2σ
nLkTr⎡
⎣⎢
⎤
⎦⎥ 1+
imsM0
M 4 / 3πr3ρ −ms( )
⎡
⎣⎢⎢
⎤
⎦⎥⎥
Chapter 3: Nucleation of Liquid Droplets
Chapter 3: Nucleation of Liquid Droplets
Nucleation on water-soluble particles Saturation ratio using the molal osmotic coefficient, assuming a
dilute solution
where and
Saturation ratio depends on salt properties (Van’t Hoff factor and molecular weight) and radius of particle
Nucleation on water-soluble particles Saturation ratio using the molal osmotic coefficient, assuming a
dilute solution
where and
Saturation ratio depends on salt properties (Van’t Hoff factor and molecular weight) and radius of particle
e
es
=expAr
−Br3
⎡⎣⎢
⎤⎦⎥≈1+
Ar
−Br3
⎛⎝⎜
⎞⎠⎟
A =2σnLkT
B =3γmsMw
nLkT
Chapter 3: Nucleation of Liquid Droplets
Chapter 3: Nucleation of Liquid Droplets
Köhler curves: Stable equilibrium: droplet will evaporate or grow
back to original radiusHaze droplets: very small particles; equilibrium less
than supersaturation, and they can deliquesce (take on water vapor)
Unstable equilibrium: an evaporating drop will grow back to it’s original size and a growing droplet will continue to grow.
Köhler curves: Stable equilibrium: droplet will evaporate or grow
back to original radiusHaze droplets: very small particles; equilibrium less
than supersaturation, and they can deliquesce (take on water vapor)
Unstable equilibrium: an evaporating drop will grow back to it’s original size and a growing droplet will continue to grow.
Chapter 3: Nucleation of Liquid Droplets
Chapter 3: Nucleation of Liquid Droplets
Köhler curves: Köhler curves:
Chapter 4 Bulk Thermodynamics of the
Atmosphere
Chapter 4 Bulk Thermodynamics of the
Atmosphere
Chapter 4: Bulk ThermodynamicsChapter 4: Bulk Thermodynamics
1st Law of Thermodynamics under moist conditions, and for a cloud-free atmosphere
Most generally, 1st law for open thermodynamic multi-phase system:
Neglecting radiation and molecular dissipation in a cloud free atmosphere the first law becomes:
1st Law of Thermodynamics under moist conditions, and for a cloud-free atmosphere
Most generally, 1st law for open thermodynamic multi-phase system:
Neglecting radiation and molecular dissipation in a cloud free atmosphere the first law becomes:
Chapter 4: Bulk ThermodynamicsChapter 4: Bulk Thermodynamics
We also introduced thermodynamic variables which are conserved for adiabatic motions: θ: Potential temperature
Conserved for dry, isentropic motions Poisson’s Equation
θl,i: Ice-liquid water potential temperature Conserved for wet adiabatic (liquid and ice transformations)
Reduces to θ in the absence of cloud or precip.
We also introduced thermodynamic variables which are conserved for adiabatic motions: θ: Potential temperature
Conserved for dry, isentropic motions Poisson’s Equation
θl,i: Ice-liquid water potential temperature Conserved for wet adiabatic (liquid and ice transformations)
Reduces to θ in the absence of cloud or precip.
d lnθ =dlnT −Ra
Cpa
⎛
⎝⎜
⎞
⎠⎟dlnp=0
di lnθil =dlnθ −Llv
cpaTdirl −
Liv
cpaTdiri =0
Chapter 4: Bulk ThermodynamicsChapter 4: Bulk Thermodynamics
θe: Equivalent potential temperature Useful in diagnostic studies as a tracer of air
parcel motions
Conserved during moist and dry adiabatic processes
θeiv is conservative over phase changes but not if precipitation fluxes exist
θe: Equivalent potential temperature Useful in diagnostic studies as a tracer of air
parcel motions
Conserved during moist and dry adiabatic processes
θeiv is conservative over phase changes but not if precipitation fluxes exist
Chapter 4: Bulk ThermodynamicsChapter 4: Bulk Thermodynamics
The first law for a moist atmosphere can be written as follows, assuming that the gas constants and heat capacities do not vary with temperature:
Neglecting heat stored in condensed water, Q(R) adn Q(D):
Assuming: drv+dirl+diri=0, we can write
The first law for a moist atmosphere can be written as follows, assuming that the gas constants and heat capacities do not vary with temperature:
Neglecting heat stored in condensed water, Q(R) adn Q(D):
Assuming: drv+dirl+diri=0, we can write
d lnθ =Rm
cpm
−Ra
cpa
⎛
⎝⎜
⎞
⎠⎟dlnp−
Llv
cpmTdrv +
Lli
cpmTdiri +
1cpm
[Q(R) +Q(D)]
d lnθ =−Llv
cpaTdrv +
Lil
cpaTdiri =0
d lnθ =Llv
cpaTdirl +
Liv
cpaTdiri
Chapter 4: Bulk ThermodynamicsChapter 4: Bulk Thermodynamics
Wet-Bulb temperature, Tw
Temperature that results from evaporating water at constant pressure from a wet bulb
Wet-bulb potential temperature, θw
Determined graphically
Conserved during moist and dry adiabatic processes (as is θe)
Energy Variables Dry static energy (s)
Moist static energy (h)
Wet-Bulb temperature, Tw
Temperature that results from evaporating water at constant pressure from a wet bulb
Wet-bulb potential temperature, θw
Determined graphically
Conserved during moist and dry adiabatic processes (as is θe)
Energy Variables Dry static energy (s)
Moist static energy (h)
Chapter 4: Bulk ThermodynamicsChapter 4: Bulk Thermodynamics Purpose of Thermodynamic diagrams
Provide graphical display of lines representing major kinds of processes to which air may be subject
Isobaric, isothermal, dry adiabatic and pseudoadiabatic processes
Three desirable characteristics
Area enclosed by lines representing any cyclic process be proportional to the change in energy or the work done during the process(in fact, designation thermodynamic diagram is reserved for only those in which area is proportional to work or energy)
As many as possible of the fundamental lines be straight
The angle between the isotherms and the dry adiabats shall be as large as possible (90º)
makes it easier to detect variations in slope
Purpose of Thermodynamic diagrams
Provide graphical display of lines representing major kinds of processes to which air may be subject
Isobaric, isothermal, dry adiabatic and pseudoadiabatic processes
Three desirable characteristics
Area enclosed by lines representing any cyclic process be proportional to the change in energy or the work done during the process(in fact, designation thermodynamic diagram is reserved for only those in which area is proportional to work or energy)
As many as possible of the fundamental lines be straight
The angle between the isotherms and the dry adiabats shall be as large as possible (90º)
makes it easier to detect variations in slope
Chapter 4: Bulk ThermodynamicsChapter 4: Bulk Thermodynamics Two diagrams meet these requirements almost perfectly
Tephigram
Skew T-log p
Two diagrams meet these requirements almost perfectly
Tephigram
Skew T-log p
Chapter 5Atmospheric Aerosols
To be continued Wednesday…
Chapter 5Atmospheric Aerosols
To be continued Wednesday…