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4. Atmospheric thermodynamics

4. Atmospheric thermodynamics. 4.1 Ideal gas law 4.2 Hydrostatic equation 4.3 First law of Thermodynamics 4.4 Adiabatic process 4.5 Second law of thermodynamics 4.6 Atmosphere as heat engine. 4.1 Gas Laws. Ideal gas equation, the equation of state ( 상태 방정식 ) PV=mRT (3.1)

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4. Atmospheric thermodynamics

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  1. 4. Atmospheric thermodynamics 4.1 Ideal gas law 4.2 Hydrostatic equation 4.3 First law of Thermodynamics 4.4 Adiabatic process 4.5 Second law of thermodynamics 4.6 Atmosphere as heat engine

  2. 4.1 Gas Laws Ideal gas equation, the equation of state (상태 방정식) PV=mRT (3.1) P: pressure (Pa), T: absolute temperature (K) V: volume(m3) , R: gas constant for 1kg ( J/kg K) m: mass (kg) For a unit mass of gas (m=1) α=1/ ρ specific volume (비적) : the volume occupied by 1kg of the gas At pressure P and temperature T P α=RT (3.3) ρ=m/V P= ρRT (3,2)

  3. 1mole: the molecular weight of the substance expressed in grams ex) 1 mol of water: 18.015 g contain the same number of molecules (NA=6.022x1023) Avogadros number

  4. Avogadro’s hypothesis : gases containing the same number of molecules occupy the same Volume at the same temperature and pressure Universal gas constant (R*) R*=8.3145 J K-1 mol-1 PV=R*T (3.5) For n moles of any gas PV=nR*T (3.6)

  5. Boltzmann’s constatn k k=R*/NA For a gas containing n0 molecules per unit volume P=n0kT For dry air Pdαd=RdT Pd :Pressure of dry air αd :specific volume of dry air Rd :Gas constant for 1kg of dry air

  6. Molecular weight of dry air mi: mass weight Mi: molecular weight Md=28.97

  7. Rd=1000R*/Md=1000·8.3145/28.97=287J K-1kg-1 For water vapor eαv=RvT Rv=1000R*/Mv=1000·8.3145/18.016=461.51J K-1kg-1 Rd/Rv=Mv/Md=ε=0.622

  8. Problem 1 • Determine the apparent molecular weight of the Venusian atmosphere, assuming that it consists of 95% of CO2 and 5% N2 by volume. • What is the gas constant for 1 kg of such an atmosphere? (Atomic weights of C, O and N are 12, 16, and 14, respectively)

  9. Dalton’s law of partial pressure : The total pressure exerted by a mixture of gases that do not interact chemically is equal to the sum of the partial pressures of the gases. P=Pd+e

  10. Virtual temperature (가온도) • 건조공기가 습윤공기와 같은 기압과 같은 밀도를 가질 때 건조공기의 온도 P = RdTv • Molecularweight Moist air < dry air • Gas constant Moist air> dry air The virtual temperature is always greater than the actual temperature

  11. 4.2 Hydrostatic equation p<0 Vertical pressure gradient force ~ gravitational force Hydrostatic equation

  12. Geopotential (지오퍼텐셜)

  13. Hypsometric equation (측고공식)

  14. Problem 2 • Calculate the thickness of the layer between the 1000- and 500hPa pressure surfaces at a point in the tropics where the mean virtual temperature of the layer is 15°C.

  15. Problem 3 A hurricane with a central pressure of 940hPa is surrounded by a region with a pressure of 1010hPa. The storm is located over an ocean region. At 200hPa the depression in the pressure field vanishes. Estimate the average temperature difference between the center of the hurricane and its surroundings in the layer between the surface and 200hPa. Assume that the mean temperature of this layer outside the hurricane is -3°C and ignore the virtual temperature correction.

  16. 4.3 The first law of thermodynamics

  17. Problem 4 • Calculate the work done in compressing isothermally 2 kg of dry air to one-tenth of its volume at 15°C.

  18. Problem5 The 1000- to 500-hPa layer is subjected to a heat source having a magnitude of 5.0106 J m-2 . Assuming that the atmosphere is at rest, calculate the resulting increase in the mean temperature and in the thickness of the layer.

  19. 4.4 Adiabatic processes (단열과정) • The change in its physical state of the system without any heat being added to or withdrawn from the system • Adiabatic process

  20. Potential temperature (온위): the temperaturethat the parcel of air would have if it were expanded or compressed adiabatically from its existing pressure and temperature to a standard ps(1000hPa)

  21. 출처: www.ecmwf.int

  22. The dry adiabatic lapse rate (건조단열감률) Hydrostatic equilibrium

  23. Saturated adiabatic lapse rate (포화단열감률) • L: Latent heat of condensation • ws: saturated mixing ratio

  24. 4.5 The second law of thermodynamics and entropy • Reversible transformation: each state of the system is in equilibrium so that a reversal in the direction of an infinitesimal change returns the working substance and the environment to their original states. • perfect differential • s: entropy (엔트로피) for reversible transformation The second law of thermodynamics

  25. 4.6 Atmosphere as heat engine Carnot cycle Initial state=final state • No change in internal energy absorbed heat =work done by the system • Net work= Q2-Q1 • Efficiency of heat engine 

  26. 1->2 Isothermal expansion Q2 is added, T2 constant 2->3 Adiabatic expansion T2-> T1 Work is done by the system 3->4 Isothermal compression Q1 is extracted, T1 constant T1 constant 4-> 1 Adiabatic compression T1->T2 Universe-review.ca/R13-09-thermodynamics06.htm

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