AOS 101 Discussion Val Bennington Ideal Gases September, 2008.
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Transcript of AOS 101 Discussion Val Bennington Ideal Gases September, 2008.
REVIEWREVIEWCOUNTOURING- YOU LOVE IT!
Helps gain a better sense of location and strength of certain past or present weather features
Time to put someone on the spot…
For temperature contouring…
Gradient: the spatial rate of change of a given field (i.e. how close are the lines together) Lines closely packed = steep gradient
For isotherms, closely packed lines (temperature gradients) = front.
For Pressure ContouringFor isobars, closely packed lines = strong
winds.
Also, winds blow nearly parallel to isobarsCounterclockwise around lows = cyclonicClockwise around highs = anticyclonic
Station Model HomeworkGenerally very good
Couple of points to make
Visibility- what is when it is clear?
Winds – label to / from
Changing gearsRobert Boyle
Was the first to analyze the behaviors of gases scientifically in the 17th century
He discovered that PV = constant if temperature is also held constant
P V
This is now known as Boyle’s Law
Jacque CharlesA French chemist who several years after
Boyle came to another important conclusion
At a constant pressure, the volume of any gas is directly proportional to the temperature:
V/T = constant
Thus, if we increase the temperature of a gas, yet keep the pressure the same, the volume will also increase.
One more French guy- Joseph Louis Gay-Lussac
- 1802
- At a constant volume, the pressure of any gas is directly proportional to the temperature (in degrees Kelvin!):
P/T = constant (at constant volume)P/T = constant (at constant volume)
- Thus, if we increase the temperature of a gas, yet keep the pressure the same, the volume will also increase.
Combining these lawsThe Ideal Gas Law
PV = nRT
Or
P = ρRT (because ρ = m/V)
This is what is used in meteorology because it makes for easier comparison by combining two variables into one
T constant: As P increases, ρ increasesP constant: As T increases, ρ decreasesρ constant: As T increases, P increases
Variable Definitions P, Pressure:P, Pressure: Force of the molecules that make up the
gas, exerted on the surface the gas is making contact with (per unit area): P = Force/Area. Units:1 mb = 1 hPa
1 hPa = 100 Pascals (Standard Unit)
T, Temperature: T, Temperature: Average kinetic energy of the molecules that make up the gas. KE = 1/2mv2 scale = (K)
ρρ, Density: , Density: Mass per unit volume (of the gas analyzed). ρ = m/V. The more molecules in a specific volume, the greater the density. (kg/m3)
R, The “gas constant for dry air”R, The “gas constant for dry air”: 287 J/kg K
Let’s try a calculationIf the temperature of an air parcel is 252.5 K, and
its density is 0.690 kg/m^3, what is the pressure of the air parcel?
From the gas law, p = ρ *R * TT = 252.5 Kρ = 0.690 kg/m^3R = 287 J/kg K
So, p = 0.690 * 252.5 * 287 = 50000 PaIn millibars, p ~ 500 mb
What Is Heat??? (Q)Heat is not the same as temperature!!!
Heat is the energy that is transferred between two objects of different temperature
If two objects both have the same temperature – the one with more mass has more heat
Measured in Joules (kg*m2/s2) or Calories
Material DifferencesYou add the same amount of heat to two
different objects (same size, both at the same initial temp)
One’s temperature increases faster than the other’s
Why???
Specific Heat (C)All materials have a specific heat
Specific heat tells us how much energy we must add in order to increase one gram of the one degree
Expressed in J / kg / K
Heat CapacityBut what if the two objects were different sizes?
Lake Michigan vs. cup of water
Which one do you need to add more heat to in order to raise the temperature?
Heat capacity is a measure of how well an object stores heat
HC = heat added / change in temp
What is Energy?
Energy is the ability to do work
The sum of all energies IS CONSTANT – it is neither created or destroyed but merely changes form (First Law of Thermodynamics)
ExamplesWater has a specific heat of 4180 J / kg / K
Air has a specific heat of 1000 J / kg K
How much heat must we add to raise 10 kg of water 10 degrees?
Q = C * m * ΔT
m = 10 kg, C = 4180 J/kg/K, ΔT=10 K
Q = 418000 J
Conduction
Heat will be transferred between two objects of different temperatures when they are TOUCHING!
Good conductors are better at transferring heat when touching other molecules (many metals)
Conduction determined by how good a conductor the material is and how large the temperature difference is between the objects
Air temperatures aloft increase because of the movement of parcels near that ground that have been warmed by the Earth
What type of heat transfer is this?
ConvectionWarm air is less dense than cooler air – so it risesIt rises until it has cooled (by expansion) to the
surrounding air’s tempImportant mechanism!!!!
Earth is heated by sun and atmosphere is warmed from below by the Earth Causes convection
Ideal Gas Law Used:Parcel of air warmer than air around it –> will
rise
As it rises, pressure exerted on it by the surrounding air decreases Volume of parcel increases (expands)
Temperature must then decrease
Parcel cools as it is lifted!
If cools to its dewpoint, will form cloud
RadiationAll objects with temperature > 0 K emit
radiation
Temperature determines what wavelengths an object emits – warmer objects emit more shorter wavelengths than a cooler object
(λmax = 2897um/ T ) (Wien’s Law)
Temp determines the amount of energy emitted by radiation (E ~ T4) (Stephan-Boltzmann’s Law)