Eats 1011 Lecture 2

From Last Lecture

• Photosynthesis
  
  • N(CO₂ + sunlight à(H₂CO)n + nO₂(day)
    
  • O₂ + H₂CO à CO₂ + H₂O(night)"burning" (energy release)
    
  • Death/burial oc C à O₂ remains in atmosphere
    
• Summary
  
  • Most of the carbon is in sedimentary rocks so that the CO₂ – N₂ **
    
  • Carbon budget(arb units)
    
    • Biosphere:
      
      • Marine: 1
        
      • Non-marine: 1
        
    • Atmosphere: 70
      
    • Ocean – dissolved : 4000
      
    • Fossil fuels : 800
      
    • Shales: 800 000
      
    • Carbonate Rocks: 2 000 000
      
  • Pressure and density
    
    • In talking of the atmosphere in a quantitative fashion we need to be concerned about certain fundamentals
      
    • Pressure, P, of a gas
      
    • Force/area = Newtons/m² = Pascal(Pa)
      
    • Two ( at least) views
      
      • Microscopic or macroscopic
        
      • Microscopic or kinetic
        
        • Collisions and rate of change of momentum
          
      • Macroscopic
        
        • The barometer, 1644
          
      • Column of mercury balances air pressure
        
      • Pressure
        
        • =weight of air / area
          
        • = mass / m²
          
        • note that as we ascend there is lenss air so that pressure decreases with altitude
          
        • surface pressure at MSL (mean sea level)
          
          • 101.32 kPa
            
          • =1013.2 mb (millibars)
            
          • =760 mm Hg = .76 metres Hg
            
          • =29.2 inches Hg
            
          • =32 feet of water approx 10 meters of water
            
          • Mass of air over 1 m² = P/g ~ 10⁵/10
            
            • = 10⁴ kg = 10 tonnes / m²
              
          • *1mb = 100 Pa = 1hPa
            
          • Back to origins
            
            • If oceans evaporated, what would the pressure be?
              
            • The weight of column of water – per square meter
              
            • Mass of water over 1 m²
              
              • Density * volume =
                
                • 10³kg/m³ x 3.2*10³ m*1m²
                  
                • =3.5 * 10⁶ kg/m²
                  
              • Weight = mass *g
                
                • ~ 3.5 * 10⁷ Pa = 350 atm
                  
• Pressure of gas = force per unit area (Pa)
  
• Boyles law, P∞ 1/v
  
  • T constant
    
  • V volume
    
• Charles Law V∞ T
  
  • P constant
    
• Combine as perfect gas law (PGL) or equation of state
  
  • P pRT
    
  • R = R*/M(gas constant)
    
  • R* = 8.314*x10³ J/K/kmole (universal gas constant
    
  • M = kg molecular weight
    
  • T = temperature in degrees Kelvin = 273.16+ T(°C)
    
• Density at MSL p = P/RT
  
  • M = kg molecular weight = 29 kg/kmole
    
  • R = R*/M
    
  • R*/29kg/ kmole = 287 J/K/kg
    
  • T = 27°C = 300K
    
  • P = P/RT = 10⁵/(287*300)
    
  • ~1.2 kg/m³
    
• Vertical Structure
  
  • Vertical variation (Z) of pressure in the atmosphere
    
  • (get diagram from website)
    
  • Stationary cylinder
    
    • Cross sectional area, A
      
    • Density, p(kg/M³)
      
  • Weight of cylinder downwards is balanced by net upward pressure force
    
  • Mass of cylinder = volume * density
    
    • DZ * Axp
      
  • Force balance (upwards)
    
    • (P + dP) * A + P * A – dZ*A*p*g = 0
      
  • Simplify
    
    • dP/dZ = -pg – Hydrostatic Law
      
  • H = RT/g(m) = 8km
    
  • P(0) = 1.013*10²kPa
    
  • P(0) = 1.2 kg/m³
    
  • P(Z) = p(0) * exp(-z/h)
    
  • p(Z) = p(0) * exp(-z/h)
    
• the higher you go upwards the less pressure in the atmosphere
  
• https://horsehead.ccs.yorku.ca/moodle/login/index.php
  
• Mean free path(λ) (the average distance between molecules calculating a distance a molecule can travel before it collides with another
  
  • Q*N* λ = 1
    
  • Q – cross section (m²)
    
  • Number density, N (molec m^-3)
    
  • Surface, λ = .3 чm
    
  • 300 km, λ = 100km (satellite drag)
    
• Vertical variation of pressure – ocean
  
  • Equation of state p = p₀*z (z<0), ie P increases linearly with depth
    
  • P doubles in z = 10 meteres, ie P(0) = p₀*g*z
    
• Vertical temperature Structure
  
  • In the stratosphere/ thermosphere temperature increases with height
    
  • In the troposphere/mesosphere it decreases
    
  • In order
    
    • Troposphere
      
    • Stratosphere
      
    • Mesosphere
      
    • Thermosphere
      
  • Temperature structure
    
    • Troposphere: 0-10/16km tropopause
      
    • Stratosphere: tropopause – 50km
      
    • Mesosphere: stratopause – 85km
      
    • Thermosphere: mesopause – 300km
      
    • Exosphere: above 300km "collisionless"
      
  • Lapse rate
    
  • ***
    
  • Homosphere
    
    • Most "inert" species are well mixed
      
  • Heterosphere
    
    • Species are in diffusive equilibrium i.e for each species there is a hydrostatic law
      
  • Ionosphere
    
    • Atmosphere is ionized by EUV