I. Physical Principles: The foundation & the tools Newton's laws: forces, pressure, motion Energy: Temperature, radiant energy II. Atmospheric & Ocean Physics: First element of climate and environmental science Atmospheric structure (T, P in "4-D") Winds, Weather, General Circulation, Climate III. Atmospheric & Ocean Biogeochemistry: Second element of climate and environmental science Atmospheric and ocean composition, past and present Human impact, global change IV. Intersection: what we know, would like to know, will never know, and what can we contribute to the debate. L-2 L-3 Road map to EPS 5 Lectures5: Pressure, barometric law, buoyancy water air fluid moves Fig. 7.6: Pressure in the atmosphere (compressible) and ocean (incompressible). Lecture 5. EPS 5: 21 Sep 2010 Review discussion of the perfect gas law from Lecture 2. 1.! Review pressure concepts: weight of overlying fluid ("hydrostatic"), force of molecules bouncing off of an object. 2.! Further discuss the concept of density ! ; 3.! Review the concept of kinetic energy of molecules in a gas. Look at some demos showing how pressure is manifest on the molecular and hydrostatic scales. 4.! Work through the concept of the barometric law (hydrostatic balance: each layer of atmosphere must support the weight of the overlying column mass of atmosphere). How does the atmosphere bring the force exerted by molecular motions into balance with the weight of overlying atmosphere? 5.! Look at the distribution of pressure with altitude in the atmosphere, or depth in the ocean. 6.! Discuss how a barometer works ("dry demo"). 7.! Introduce buoyancy. water air fluid will start to move Water columns have the same height: Pressures equal on both sides. Water columns higher on the left: Pressure higher on the left. Cylinder volume = h x A = h x " r2. Mass = ! h " r2. Weight = Mass x g = ! h " r2 Mass of water = volume x density; Which has the greater volume? Pressure = Mass x g / A = h ! gPerfect gas law (a.k.a. Boyle's and Charles' Laws) PV = NkT where P is pressure, V volume, N the number of molecules in the volume, and T the absolute temperature (Kelvin; T(K)=T(C)+273.15); k is Boltzmann's constant (1.38 x 10-23 Joules/Kelvin). Boyle’s law P1V1 = P2 V2 ; Charles’ Law P1/ T 1 = P2/ T2 P = nkT, where n (= N/V, the number density) is the number of molecules per unit volume. The Perfect Gas Law relates pressure to temperature (the kinetic energy of the molecules) and "number density". The density ( ! ) is defined as the mass per unit volume. If m is the mass of one molecule, then ! = m n . The pressure, density and temperature of air are therefore related by: P = ! (k/m) T = ! R T , an important form of the perfect gas law. The constant (k/m) is called “R” (the gas constant), "R" = 287.5/M J kg-1 K-1. Lecture 5. EPS 5: 21 Sep 2010 1.! Review pressure concepts: weight of overlying fluid ("hydrostatic"), force of molecules bouncing off of an object. 2.! Discuss the concept of density ! ; 3.! Review the concept of kinetic energy of molecules in a gas. Look at some demos showing how pressure is manifest on the molecular and hydrostatic scales. 4.! Work through the concept of the barometric law (hydrostatic balance: each layer of atmosphere must support the weight of the overlying column mass of atmosphere). How does the atmosphere bring the force exerted by molecular motions into balance with the weight of overlying atmosphere? 5.! Look at the distribution of pressure with altitude in the atmosphere, or depth in the ocean. 6.! Discuss how a barometer works ("dry demo"). 7.! Introduce buoyancy. Kinetic energy and molecular motion E = 1/2 m v2 = 3/2 k T k = 1.38 # 10-23 Joules/Kelvin; T = 300 K (room temperature) E = 6.21 # 10-21 Joules/molecule; for one mole, N0 (6.02 # 1023 molecules): E0 = 3738.42 Joules/mole. Thus the molecules in only 29 grams of air (1 mole) contain 3.78 kJ of kinetic energy. Since 1 Watt = 1 Joule/s, this amount of energy fires up the electrical appliances in an average house for 1 second! How fast do molecules move? 3/2 kT = 1/2 mv2 mair = 29/N0 = 4.83 # 10-26 kg per molecule v = (3 kT/ m )1/2 = 500 m s-1 at T=300 K A more exact treatment gives (8 kT/("m))1/2 = 467 m s-1 . This is the speed of sound! (why is that?) Lecture 5. EPS 5: 21 Sep 2010 1.! Review pressure concepts: weight of overlying fluid ("hydrostatic"), force of molecules bouncing off of an object. 2.! Discuss the concept of density ! ; 3.! Review the concept of kinetic energy of molecules in a gas. Look at some demos showing how pressure is manifest on the molecular and hydrostatic scales. 4.! Work through the concept of the barometric law (hydrostatic balance: each layer of atmosphere must support the weight of the overlying column mass of atmosphere). How does the atmosphere bring the force exerted by molecular motions into balance with the weight of overlying atmosphere? 5.! Look at the distribution of pressure with altitude in the atmosphere, or depth in the ocean. 6.! Discuss how a barometer works ("dry demo"). 7.! Introduce buoyancy.Atmospheric pressure and temperature Distribution of pressure with altitude: the barometric law. Changes in pressure with altitude in the atmosphere (left) and depth in the ocean (right). Pressure always increases as the observer moves downward because the weight of the overlying column of fluid (air or water) increases. Note: Altitude is conventionally measured increasing upwards from the surface of the earth, and depth increasing downwards. Therefore pressure decreases with increasing altitude in the atmosphere and pressure increases with increasing depth in the ocean. "air is compressible" ! density depends on pressure ! = P/ [ (k/m) T ] atmosphere ocean Z 2 Z 1 D 2 D 1 P 1 P 1 P 2 P 2 Z (altitude) increases upward P 1 > P 2 at Z 1 < Z 2 D (depth) increases downward P 1 > P 2 at D 1 > D 2 Z 2 Z 1 P 1 P 2 By how much is P1 > P2? The weight of the slab of fluid between Z1 and Z2 is given by the density, !, multiplied by volume of the slab) and g weight of slab = !#(area # height) #g. Set the area of the column to 1 m2, the weight is ! g # (Z2 -Z1): If the atmosphere is not being accelerated, there must be a difference in pressure (P2 - P1) across the slab that exactly balances the force of gravity (weight of the slab). Relationship between density, pressure and altitude !g gravity Net P1 – P2 - (P2 - P1) = weight = ! g #(Z2 -Z1). Pressure increases