Phys Met Short Answer Flashcards
Charles’ Law
V1/T1 = V2/T2
Concept: Describes how gas expands when heated at constant pressure.
Boyle’s Law
P1V2 = P2V2
Concept: Explains how increasing the pressure on a gas decreases its volume if the temperature remains constant
Universal Gas Constant (R) vs. Specific Gas Constant (R)*
Universal Gas Constant: R* = 8.314J/molK
Specific Gas Constant: R = R/ Molar Mass of Gas
Gas Constant for Dry Air (Rd): 287 J/kgK
Gas Constant for Dry Air (R_v): 461 J/kgK
Similarities: All derived from R. R is being divided by the mass of the gas
Differences: Each R is used for specific things (Rd for dry air for example) ; values lol ; R* provides a general reference for gases
Ideal Gas Law (Moist & Dry Air)
Dry Air: P = pRdT
Moist Air: P = pRTv
p = density ; Rd = dry gas constant ; T = Temperature ; Tv = Virtual Temp
Dry Ideal Gas Law: The Ideal Gas Law for dry air tells us that pressure is directly proportional to the density and temperature of dry air. This equation helps determine the air’s density at different pressures and temperatures.
Moist Ideal Gas Law: The Ideal Gas Law for moist air describes how the total pressure of moist air depends on its density and virtual temperature. By using the virtual temperature, we can apply the Ideal Gas Law to situations involving varying moisture levels, which affects air buoyancy, stability, and density.
Avogadro’s Law
V1/n1 = V2/n2
V = Volume ; n = amount of moles (if k is provided, it is a constant)
Concept: Equal volumes of different gases contain equal numbers of molecules under the same temperature and pressure.
Dalton’s Law
∑ P (P1+P2+P3…)
P = Partial pressures of the individual gases.
Concept: The total pressure of a gas mixture equals the sum of each gas’s partial pressure.
Virtual Temperature
Tv = T(1+0.608w)
T = Actual temp (typically in K) ; w = Mixing ratio (g/kg kg/kg)
Concept: Temperature that dry air would need to match the density of moist air.
Hydrostatic Equation
dP/dz = -pg
p = liquid density ; q = 9.81 m/s^2
Concept: Describes the balance between the upward force of air pressure and the downward force of gravity. Explains why atmospheric pressure decreases with height and helps estimate pressure changes vertically.
Geopotential vs. Geometric Height
Geopotential Height: Adjusted for variations in gravity with altitude.
Geometric Height: Direct measurement above sea level.
What It Tells Us: Geopotential height is more practical in meteorology for comparing energy changes with altitude.
Hypsometric Equation
Z2-Z1 = (RT)/g ln(P1/P2)
R = Gas constant ; T = Mean temperature (in K) ; g = 9.81 m/s^2 ; P1/ P2 = pressure values
Concept: Relates pressure difference to temperature and height in the atmosphere.
Equivalent Barotropic Structures
Concept: Barotropic structures mean temperature is uniform horizontally at any given level. In baroclinic structures, temperature varies horizontally. Helps distinguish between stable systems and those with vertical temperature gradients, affecting atmospheric circulation.
Examples: Barotropic—tropical storms; Baroclinic—mid-latitude cyclones.
Reduction to Sea Level Pressure
Standardizes pressure readings to sea level to allow for consistent comparisons across locations at different altitudes.
First Law of Thermodynamics
ΔU = Q + W
ΔU = change in internal energy, U ; Q = the sum of all heat transfer into and out of the system ; W = the net work done on the system
Concept: Energy conservation principle for systems. Describes how adding heat affects internal energy and work done on/by the atmosphere.
Enthalpy
H = U + pV
U = internal energy ; p = pressure ; V = volume
Concept: The total heat content in a system at constant pressure. Reflects the energy stored and exchanged in atmospheric processes.
Potential Temperature (θ)
θ = T(p0/p)^R/Cp
T = Actual temp ; p0 = reference pressure (typically 1000 hPa) ; p = pressure ; R/Cp = 0.286
Concept: The temperature an air parcel would have if brought adiabatically to p0.
Equivalent Temperature & Equivalent Potential Temperature
Equivalent Temperature (𝑇𝑒): Accounts for all latent heat released if all water vapor condensed.
Equivalent Potential Temperature (𝜃𝑒): Potential temperature accounting for the energy released by condensation.
What It Tells Us: Both are essential for studying cloud formation and convective stability.
Poisson’s Equation
T = T(p/p0)^0.286 ?
Concept: Describes the temperature change in an adiabatic process based on pressure changes.
Adiabatic and Pseudoadiabatic Processes
Adiabatic: No heat is exchanged with surroundings.
Pseudoadiabatic: Moisture is lost by condensation.
What It Tells Us: Crucial for understanding temperature and moisture changes in the atmosphere.
Atmospheric Stability & Convective Instability
Stability: Determines if air parcels return to their original state or continue rising.
Convective Instability: When warm air rises due to being less dense than the air above it.
Clausius-Clapeyron Equations
(Lv/RvT^2)
Lv = 2.510^6 ; Rv = 461.5 ; T = Temp
Concept: Describes how saturation vapor pressure changes with temperature.
What It Tells Us: Key to understanding humidity and phase changes like evaporation and condensation.
Absolute Humidity, Specific Humidity, and Mixing Ratio
Absolute Humidity measures the actual density of water vapor in a given volume.
[mv/ V (mv = Mass of water vapor; V = volume)]
Specific Humidity expresses the amount of water vapor relative to the total air mass.
[mv/md+mv (md = mass of dry air)]
Mixing Ratio expresses the amount of water vapor relative to the mass of dry air.
[mv/md]
First Law of Thermodynamics Special Cases
Isobars: Lines of equal pressure. Horizontal lines seen on a Skew-T.
Isotherms: Lines of equal temperature. Isotherms are the diagonal lines like /.
Dry Adiabats: Nearly straight curves that form a diagonal like . Constant potential temperature.
Pseudoadiabats: Curved lines (typically green) starting from the bottom and curving into the upper left. Lines of constant equivalent potential temp/ wet bulb potential temp
Mixing Ratio: Dotted lines similar to the isotherms /, but are steeper. Lines of constant moisture (water vapor)
Entropy
Concept: Measure of disorder or randomness in a system. Reflects energy dispersal in the atmosphere, guiding weather system analysis.
Second Law of Thermodynamics
Concept: States that entropy always increases in an isolated system. Tells us the direction of energy flow and how energy disperses.
Thermodynamic Diagrams (Skew-T)
Concept: Visualizes temperature, pressure, and other variables to analyze atmospheric conditions. Useful for assessing stability, temperature gradients, and potential weather changes.
How to plot curve for a theoretical parcel
First, determine the location of the LCL and LFC. From the LFC, you will follow along the PSEUDOADIBATS/ WET ADIEBATS. These are the green curved lines that curve to the left. You will follow that until you hit the air temperature.
How to find LCL
Find the dew point temp at the lowest pressure value (typically 1000 mb or 900 mb or whatever). Follow along the DOTTED MIXING RATIO lines from that initial dew point value.
Then, find the initial air temperature value. Similarly, follow the DRY ADIABAT until it crosses the mixing ratio line from the dew point. Create a horizontal line and note the pressure value.
How to find LFC
From your LCL value, follow the WET ADIABAT line until it intersects the air temperature (not always possible).
How to find CAPE
This is the area between the theoretical parcel curve and air temperature. CAPE will be above the LFC and below the EL.
How to find CIN
CIN is the area between the air temp and parcel curve, and will be below the LFC, but the parcel curve is to the LEFT of the air temperature and will be below the LFC.
How to find EL
This is where the parcel curve intersects the air temperature (if possible).
How to find the KI
KI = T850 - T500 + Td850 - (T700-Td700)
How to find the LI
LI = T500 - T500(parcel)
How to find FRL
Follow the 0 degree isotherm and follow it until it reaches the air temperature
How to find the wet bulb temperature/ potential wet bulb temp.
Follow the wet adiabat under the LCL. Where that line hits at the bottom of the Skew-T will be your WBT.
How to find potential temperature
From the initial point, move down along a dry adiabat line until you reach the 1000 mb level.
How to find the equivalent potential temperature
From the LCL, follow the moist adiabat downward to a pressure level of 1000 mb.
Absolutely stable vs Conditionally unstable vs absolutely unstable vs convectively unstable layer
Absolutely Stable: Environmental temperature profile slopes to the right of both dry and moist adiabats.
Conditionally Unstable: Environmental temperature profile slopes between dry and moist adiabats.
Absolutely Unstable: Environmental temperature profile slopes to the left of both dry and moist adiabats.
Convectively Unstable: Occurs when lapse rate of the moist air is greater than that of the dry air in a layer
How to find Theta-e on Skew-T
Find the temperature and dew point at the pressure given.
