AOS 101 DiscussionAOS 101 DiscussionVal BenningtonVal Bennington

Ideal GasesSeptember, 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

Ideal Gas Tutorial

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

Heat Transfer

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

Heat TransferConduction

Convection

Latent Heating

Radiation

Advection

You touch a warm pot on the stove and get a burn

What is this form of heat transfer????

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

Winds blow in warmer air

What type of heat transfer is this?

AdvectionWarm air advection when we expect the winds to

warm our region over time

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

The sun warms the Earth, but they aren’t touching

What mechanism is responsible for this???

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)

RadiationShorter wavelengths carry more energy!

I am freezing cold after I get out of the swimming pool

Why am I losing heat?

Latent HeatIt takes energy to change water from a liquid to

a gas

Your body supplies that heat when you get out of the pool and you cool off

Why do you dry off faster in a desert climate?