Ideal Gas Law AOS 101 Discussion Sections 302 and 303 upload.wikimedia.org planetoddity.com

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)

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 KE avg

Temperature T1T1 > T2T2 KE avg 1 KE avg2 > > Assuming that m 1 = m 2 v1v1 v2v2 >

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 =ρ =

Density Which box has the greater density ( ρ = m/V)? = 1 kg 1 m Box 1 Mass: 5 kg Volume: 1 m 3 Box 2 Mass: 15 kg Volume: 1 m 3 Density: 5 kg/m 3 Density: 15 kg/m 3 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) 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 Java applet chemwiki.ucdavis.edu

Ideal Gas Law P = ρ RT Pressure 1 mb = 1 hPa = 100 Pa Density Air ≈ 1000 kg/m 3 Ocean ≈ 1056 kg/m 3 Temperature 0 ° C = K Gas Constant 287 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 martine.people.cofc.edu

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 applet Java applet blog.gaiam.com whatscookingamerica.net

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 constant bfgoodrichtires.com

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 Java applet

An Air Parcel  An invisible, imaginary, and infinitely elastic container  Usually a cubic meter in size (1 m 3 )  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 voices.washingtonpost.com upload.wikimedia.org