AOS 101 Discussion Val Bennington

1. AOS 101 DiscussionVal Bennington Ideal Gases September, 2008

2. REVIEW • COUNTOURING- 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…

3. 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.

4. For Pressure Contouring • For isobars, closely packed lines = strong winds. • Also, winds blow nearly parallel to isobars • Counterclockwise around lows = cyclonic • Clockwise around highs = anticyclonic

5. Station Model Homework • Generally very good • Couple of points to make • Visibility- what is when it is clear? • Winds – label to / from

6. Changing gears • Robert 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

7. Jacque Charles • A 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.

8. 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) - Thus, if we increase the temperature of a gas, yet keep the pressure the same, the volume will also increase.

9. Combining these laws • The 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 increases P constant: As T increases, ρ decreases ρconstant: As T increases, P increases

10. Variable Definitions • 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: Average kinetic energy of the molecules that make up the gas. KE = 1/2mv2 scale = (K) • ρ, 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”: 287 J/kg K

11. Ideal Gas Tutorial

12. Let’s try a calculation • If 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 * T • T = 252.5 K • ρ = 0.690 kg/m^3 • R = 287 J/kg K • So, p = 0.690 * 252.5 * 287 = 50000 Pa • In millibars, p ~ 500 mb

13. Heat Transfer

14. 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

15. Material Differences • You 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???

16. 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

17. Heat Capacity • But 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

18. 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)

19. Examples • Water 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

20. Heat Transfer • Conduction • Convection • Latent Heating • Radiation • Advection

21. You touch a warm pot on the stove and get a burn • What is this form of heat transfer????

22. 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

23. Winds blow in warmer air What type of heat transfer is this?

24. Advection Warm air advection when we expect the winds to warm our region over time

25. 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?

26. Convection Warm air is less dense than cooler air – so it rises It rises until it has cooled (by expansion) to the surrounding air’s temp Important mechanism!!!! Earth is heated by sun and atmosphere is warmed from below by the Earth  Causes convection

27. 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

28. The sun warms the Earth, but they aren’t touching • What mechanism is responsible for this???

29. Radiation • All 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)

30. Radiation Shorter wavelengths carry more energy!

31. I am freezing cold after I get out of the swimming pool • Why am I losing heat?

32. Latent Heat • It 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?