Brief

Large parts of this work were accomplished without funding. If you find the information on this site helpful, please consider donating to this project.

 

The Physics of Gas Temperature in the Vortex Tube

To understand the governing physical laws of vortex tubes, we need to first understand gas temperature. 

What is static temperature?

Gas temperature is measured with thermometer, when at rest with respect to the gas. This is the temperature, thermodynamic temperature or static temperature of the gas Ts.

cloud_t_mov

What is total temperature?

Total temperature T of gas is introduced for the more general case of moving gas and stationary thermometer:

gas_stopping

T is known as total temperature or stagnation temperature.

What is the definition of total temperature?

def_T1

The meaning of this definition is: When moving gas is brought to rest adiabatically, its static temperature rises by c2/(2cp), where c is the velocity of the initially moving gas, before it was forced to stop; cp is the isobaric heat capacity of the gas. This value of the static temperature is called "total" or "stagnation" temperature, because it is a result of the initial static temperature while the gas was still moving plus its rise after the gas was forced to stop adiabatically.

How does one measure total temperature?

There is no thermometer that can measure total temperature. Thermometers are designed to measure static, or thermodynamic temperature only. Total temperature is an effective temperature; it is a sum of entities that have units of temperature.

It is important to understand the difference between static temperature Ts and total temperature T of gas. This is crucial knowledge in the understanding of the vortex tube effect.

Is static temperature frame-dependent?

By definition, the static temperature Ts is the same in all frames of reference

Is total temperature frame-dependent?

Yes, it is.  The total temperature T is not the same in all inertial frames of reference, as it depends on the velocity of the gas c.

Large parts of this work were accomplished without funding. If you find the information on this site helpful, please consider donating to this project.

 

The information contained in this site is based on the following research articles written by Jeliazko G Polihronov and collaborators:

Questions about this site? Email Jeliazko G. Polihronov at:

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