Ideal Gas Law

AOS 101 Discussion Sections 302 and 303

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State Variables State variables are quantities that tell us the

state of a gas Specifically, the atmosphere

Examples of state variables Temperature (T) Pressure (P) Density (ρ) Volume (V) Mass (m) Energy (E)

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Temperature The temperature of a substance is a

proportional to the average kinetic energy of the molecules in that substance If the temperature increases, the kinetic energy

increases If the temperature decreases, the kinetic energy

decreases T α KEavg

Temperature

T1 > T2

KEavg1 KEavg2

>

>

Assuming that m1 = m2v1 v2>

Temperature in the Atmosphere Troposphere

Temperature decreases with height

~10 km Tropopause

Temperature is constant with height

Stratosphere Temperature increases

with height ~45 km

Stratopause Mesosphere

Temperature decreases with height

~80km Mesopause Thermosphere

Density The density of a substance is defined as the

amount of mass of a substance in a given volume

Density =

ρ =

Density

Which box has the greater density (ρ = m/V)?

= 1 kg

1 m

1 m

1 m

Box 1Mass: 5 kg

Volume: 1 m3

Box 2Mass: 15 kg

Volume: 1 m3

Density: 5 kg/m3

Density: 15 kg/m3

Box 2 is more dense

Density in the Atmosphere Air molecules

decrease in number as you move further away from the Earth’s surface

Density decreases with height

How density changes with altitude (baseball analogy)

Pressure The air pressure is the force per unit area that

the atmosphere exerts on any surface it touches

In this class, we say that the force is the weight on an object

Pressure =

P =

Pressure

Which of these scenarios has the most pressure exerted on the terrain?The mountain has less mass above it than the grassy field,

since the atmosphere is most dense near its surface.

Therefore, using F=mass*gravity and P= force/area, the pressure exerted on the grassy field is greater than that of the pressure exerted on the mountain.

Pressure in the Atmosphere Pressure always,

always, ALWAYS decreases with height

Pressure decreases exponentially with height

Relationship between P, T, and ρ Java applet

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Ideal Gas Law

P = ρRTPressure1 mb = 1 hPa = 100 Pa

DensityAir ≈ 1000 kg/m3

Ocean ≈ 1056 kg/m3

Temperature0 °C = 273.15 K

Gas Constant287 J/K·kg

What is an Ideal Gas, anyway? An ideal gas is a gas in which the molecules

move randomly and do not interact with each other

Most gases do behave like an ideal gas Ideal gas law is not suitable for low

temperatures or high pressures Because of phase changes

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Holding a Parameter Constant The parameter is unchanging and can be

conceptually ignored Symbolizing the affect of holding a parameter

constant x α y – x is directly proportional to y x α 1/y – x is inversely proportional to y

Examples using P=ρRT Holding density (ρ) constant

P α T Holding pressure (P) constant

T α 1/ρ Holding temperature (T) constant

P α ρ

Constant Pressure (T α 1/ρ)

Think of an infinitely elastic balloon If you heat the balloon, what happens? How does this affect the kinetic energy?

Think of boiling water in a pot What happens to the water as it is heated? What happens when the water reaches the

surface? Java appletblog.gaiam.c

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Constant Temperature (P α ρ)

Think about filling up a tire What are you adding to the

tire? How does this change the

pressure? Think about a leaking balloon

What is the balloon losing? Now, how does this change the

pressure? How do either of these

change the kinetic energy? Remember, temperature is

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Constant Density (P α T)

Most common parameter to be kept constant Think about the car from the previous

homework Finding the initial footprint

Weight = 1920 lbs and P = 30 psi (lbs/sq in) Use P=Weight/Area to find overall footprint

Going from August to January What happens to the temperature? How does this affect the pressure?

Calculate the final footprint (assuming idealized tires)

Java applet

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An Air Parcel An invisible, imaginary, and infinitely elastic

container Usually a cubic meter in size (1 m3)

It is used to “test” the atmosphere It does not actually occur in nature Can be used to determine how a portion of the

atmosphere evolves Can be roughly shown with weather balloons Shows atmospheric instability

Extremely useful when studying heat and energy exchange in the atmosphere

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