Physical Fundamentals of Global Change Processes

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1 University of Applied Sciences Eberswalde Master Study Program Global Change Management Manfred Stock Potsdam Institute for Climate Impact Research Module: Physical Fundamentals of Global Change Processes 28 November Lecture 6 a)energy balance, energy efficiency, thermodynamics; b) Discussion about open questions of past lectures and the following oral presentations Global Change Fundamentals 6-1

2 Energy = "the potential for causing changes." There are several types of energy: Examples associated with kinetic energy motion E kin = ½ m v² potential energy position, work E pot = R1 R2 F(r) dr internal energy atomic speed du = δq + δw thermal energy temperature T = TdS + pdv heat Q, entropy S radiant energy chemical energy radiation, luminosity = E/t L = 4πR² σ T 4 [ W ] chemical bonds, type of potential energy Global Change Fundamentals 6-2

3 INSOLATION and Greenhouse Energy Balance 4π R² IR- Radiation E GAIN = π R² S 0 (1- α) + G F E LOSS = 4 π R² σ T 4 T(S,α,G F ) E GAIN = E LOSS T = (G F /σ +(1-α)S 0 /4σ) 1/4 = 288 K Insolation π R² S 0 S 0 = W/m² σ = 5.67e-8 Wm -2 K -4 α = 0.3 G F = W/m² Greenhouse flux Global Change Fundamentals 6-3

4 Layers of the Atmosphere Global Change Fundamentals 6-4

5 Global atmospheric flux processes Global Change Fundamentals 6-5

6 Task: Calculate the Mass of the Atmosphere The complex way: M at = ρ(λ,θ,h) dλ dθ dh = F E * ρ(h) dh The simple way: with M at = F E * p(0) /g = 5.27e18 kg F E = 4 π R E ² = 5.105e14 m² R E = 6.373e6 m p(0) = 101,325 Pa (Pa = kg m -1 s -2 ) g = 9.81 m/s² Global Change Fundamentals 6-6

7 Water Vapor Pressure p V = n R T R = J K -1 mol -1 Clausius-Clapeyron Equation: dp/dt = (S g S f )/(V g V f ) dp Q Q = dt (V g V f ) T V g T heat of evaporation: Q = U + p V = 2088 kj/kg kj/kg = 2.26 MJ/kg Global Change Fundamentals 6-7

8 Task: Calculate the order of magnitude of the mass of water in the atmosphere and its evaporation energy The simple way: M at = F E * p(0) /g = 5.27e18 kg M w = M at p w /p(0) m w /m at = 1.25e16 kg E w = M w * Q = 2.82e22 J = 7,84e15 kwh with m w /m at = 18/30 p w (-5 C) = 400 Pa (Pa = kg m -1 s -2 ) Q = 2.26 MJ/kg World energy demand: 1.07e14 kwh/a Terrestrial solar energy: 1.49e22 kwh/a Global Change Fundamentals 6-8

9 Global Hydrological Cycle: Reservoirs (10³ km³) and Flux (10³ km³/a) D (1997) Global Change Fundamentals 6-9

10 Tropical cyclone = Carnot cycle The thermodynamic structure of the hurricane can be modelled as a heat engine running between sea temperature of about 300K and the tropopause which has temperature of about 200K. Parcels of air traveling close to the surface take up moisture and warm, ascending air expands and cools releasing moisture (rain) during the condensation. This release of latent heat energy during the condensation provides mechanical energy for the hurricane. Both decreasing temperature of upper troposphere or increasing temperature of atmosphere close to the surface will increase on maximum winds observed in hurricanes. When applied to hurricane dynamics it defines Carnot heat engine cycle and predicts maximum hurricane intensity. Global Change Fundamentals

11 Real Heat Engines Carnot Cycle A real engine (left) compared to the Carnot cycle (right). The entropy of a real material changes with temperature. This change is indicated by the curve on a T-S diagram. For this figure, the curve indicates a vapor-liquid equilibrium (Rankine cycle). Irreversible systems and losses of heat (for example, due to friction) prevent the ideal from taking place at every step. Maximum energy efficiency = Carnot efficiency = η = (T H T C )/T H Global Change Fundamentals

12 Thermodynamics 1. In any process, the total energy of the universe remains constant. 2. There is no process that, operating in a cycle, produces no other effect than the subtraction of a positive amount of heat from a reservoir and the production of an equal amount of work. 3. As temperature approaches absolute zero, the entropy of a system approaches a constant. de - T ds + p dv 0 Global Change Fundamentals

13 Thermodynamic systems and Heat Engine Processes Thermodynamic systems: - isothermal: at constant temperature, maintained with heat added or removed from a heat source or sink - isobaric: at constant pressure - isometric/isochoric: at constant volume - : no heat is added or removed from the system during process Cycle/Process Compression Heat Addition Expansion Heat Rejection Carnot isothermal isothermal Otto (Petrol/Gasoline) isometric isometric Diesel isobaric isometric Brayton (Jet) isobaric isobaric Stirling isothermal isometric isothermal isometric Ericsson isothermal isobaric isothermal isobaric Global Change Fundamentals