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The concept of potential temperature is easy to define, but the simplicity of its definition should not
detract from its great significance in meteorological analysis.
The potential temperature of a parcel of dry air is the temperature that parcel would have if its pressure
were changed through adiabatic processes to a standard pressure, usually 1000 mb (100 kPa).
Adiabatic processes are ones that involve no exchange of heat between the parcel and its environment and thus leave the entropy of the parcel unchanged. Therefore parcels with the same potential temperature have the same entropy per unit mass. In other words, potential temperature and entropy per unit mass are equivalent measures of the state of a parcel of dry air.
The actual computation of the potential temperature of a parcel is achieved through the use of the Poisson Relations; i.e.,
where p and T are the actual pressure and absolute temperature of the parcel and pstandard is the standard pressure, usually 1000 mb. The parameter κ is equal to 2/7 for an ideal gas, which is a good approximation for dry air.
For example, if the actual pressure and temperature of a parcel of dry air are 800 mb and 250 K, respectively then the potential temperature θ is
This says that if the parcel were adiabatically compressed from 800 mb to 1000 mb it temperature would increase
by 15.46° to 266.46 K.
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