The potential temperature is the temperature of the gas , adiabatically reduced to standard pressure , usually 10 5 Pa . Denoted by the Greek letter and is expressed through the following equation, also called the Poisson equation :
Where - temperature in Kelvin , - gas constant and - specific heat in the isobaric process .
Derivation of the equation
We use the equation of the first law of thermodynamics :
Where denotes the change in enthalpy , - absolute temperature - entropy change, - specific volume and - pressure. For adiabatic processes, the change in entropy is zero, and the equation takes the form:
Substitute in the above expression the equation of state of an ideal gas
and also considering that
we get
After integration we have:
Expressing from here we get:
It is useful to take into account that
- where - adiabatic index .
The concept of potential temperature is used in meteorology . A similar concept, taking into account the equation of state of sea water, is in oceanology .
See also
- Adiabatic temperature gradient