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CLIMATE/EARTH 401�Geophysical Fluid Dynamics�Dynamical Meteorology

Richard B. Rood

rbrood@umich.edu

https://clasp.engin.umich.edu/people/richard-b-rood/

https://openclimate.org/

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Thermodynamic Equation for the Atmosphere

  • This lectures requires you to be familiar with the conservation of energy and the introductory material on thermodynamic energy.

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Conservation of thermodynamic energy

  • Change in internal energy is equal to the difference between the heat added to the system and the work done by the system.
  • Internal energy is due to the kinetic energy of the molecules.
  • Total thermodynamic energy is the internal energy plus the energy due to the parcel moving.

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Thermodynamic Equation

Refer to lecture relating enthalpy, entropy, and the work done by the system (expansion and contraction).

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Thermodynamic Equation

J is the source or sink of heating which are:

    • Radiation (solar and infrared)
    • latent heat release (phases of water)
    • thermal conductivity
    • frictional heating�

α = 1/ρ is the specific volume�cv = 717 J K-1 kg-1 is the specific heat of dry air at � constant volume

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Another form of the Thermodynamic Equation

cp = 1004 J K-1 kg-1 is the specific heat of dry air at constant pressure��Note: cp = cv + Rd = 1004 J K-1 kg-1

�Rd = 287 J K-1 kg-1 gas constant for dry air

Can be derived via the ideal gas law:

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Different forms of the thermodynamic equation

(Divide by T)

Use equation of state�(ideal gas law)

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Different forms of the thermodynamic equation

For conservative motions �(no heating, dry adiabatic: J = 0):

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End: Thermodynamic Equation for the Atmosphere

Richard B. Rood

rbrood@umich.edu

https://clasp.engin.umich.edu/people/richard-b-rood/

https://openclimate.org/