The potential temperature of a parcel of air at pressure P is the temperature that the parcel would acquire if adiabatically brought to a standard reference pressure P₀, usually 1 bar. The special temperature is denoted θ and is often given by In thermodynamics, an adiabatic process is a process in which no heat is transferred to or from working fluid. ...

,

where T is the current temperature of the parcel, R is the gas constant of air, and c_p is the specific heat capacity at a constant pressure. Fig. ... The gas constant (also known as the universal or ideal gas constant, usually denoted by symbol R) is a physical constant used in equations of state to relate various groups of state functions to one another. ... The specific heat capacity (symbol c or s, also called specific heat) of a substance is defined as heat capacity per unit mass. ...

Comments

Potential temperature is a more dynamically important quantity than the actual temperature. Under almost all circumstances, potential temperature increases upwards in the atmosphere, unlike actual temperature which may increase or decrease. Potential temperature is conserved for all dry adiabatic processes thus it is an important quantity in studying atmosphere (which is often very close to being dry adiabatic).

Contexts

The concept of potential temperature applies to any compressible fluid. It is most frequently used in the Atmospheric sciences, but also in Oceanography[1]. Atmospheric sciences is an umbrella term for the study of the atmosphere, its processes, the effects other systems have on the atmosphere, and the effects of the atmosphere on these other systems. ... Thermohaline circulation Oceanography (from Ocean + Greek γράφειν = write), also called oceanology or marine science, is the branch of physical geography that studies the Earths oceans and seas. ...

Potential Temperature Perturbations

The atmospheric boundary layer (ABL) potential temperature perturbation is defined as the difference between the potential temperature of the ABL and the potential temperature of the free atmosphere above the ABL. This value is called the potential temperature deficit in the case of a katabatic flow, because the surface will always be colder than the free atmosphere and the PT perturbation will be negative. In physics and fluid mechanics, the boundary layer is that layer of fluid in the immediate vicinity of a bounding surface. ... See katabatic wind, a wind which blows down a topographical incline. ...

Derivation

The enthalpy form of the first law of thermodynamics can be written as: In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as Δ or ΔH, or rarely as χ) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the useful work obtainable from a closed thermodynamic system under constant conditions. ... Thermodynamics (from the Greek thermos meaning heat and dynamics meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ...

dh = Tds + vdp,

where h denotes the enthalpy change, T the temperature, ds the change in entropy, v the specific volume, and p the pressure. In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as Δ or ΔH, or rarely as χ) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the useful work obtainable from a closed thermodynamic system under constant conditions. ... Ice melting - classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice. ...

For adiabatic processes, the change in entropy is 0 and the 1st law reduces to:

dh = vdp.

For approximately ideal gases, such as the dry air in the earth's atmosphere, the equation of state, pv = RT can be substituted into the 1st law yielding, after some rearrangement:

,

where the dh = c_pdT was used and both terms were divided by the product pv

Integrating yields:

,

and solving for T₀, the temperature a parcel would acquire if moved adiabatically to the pressure level p₀, you get:

.

External links

• http://scienceworld.wolfram.com/physics/PotentialTemperature.html
• http://meted.ucar.edu/awips/validate/thetae.htm

Bibliography

• M K Yau and R.R. Rogers, Short Course in Cloud Physics, Third Edition, published by Butterworth-Heinemann, January 1, 1989, 304 pages. EAN 9780750632157 ISBN 0-7506-3215-1