Adiabatic and Quasistatic Compression

[Identity]

In "Introduction to Thermal Physics" - Schroeder, the derivation for adiabatic compression: $$V^\gamma P = \mbox{constant}$$ is derived by assuming the compression is still slow enough to be quasistatic.

However, I'm still a bit confused with how slow is 'slow'.

Quasistatic compression needs to be slow enough for the gas to respond:
$$0< v_{QC} < v_{speed\ of\ sound\ in\ gas}$$

Adiabatic compression requires it to be fast enough for no heat to escape... what are the upper and lower limits for adiabatic compression?

And what happens to the formula for adiabatic compression when we compress faster than quasistatic compression?

Thx

 

[Mapes]

Quastistatic compression should actually be much slower than the speed of sound, slow enough to avoid turbulence. The idea is that the gas is kept in an equilibrium state at all times, so we have a well-defined thermodynamic path from beginning to end.

The necessary speed for adiabatic compression depends upon the heat transfer properties of the enclosure, and is somewhat arbitrary; perhaps you want a <1% or <5% temperature disturbance due to heat transfer during the process.

There's no guarantee that the minimum adiabatic speed is less than the maximum quasistatic speed, but it's normally assumed in introductory thermo classes that such a "happy window" exists.

 

[Identity]

Thanks mapes :)

 

[DrDu]

...then you have to explain to me why the adiabatic compression formula is usually used to derive the speed of sound in a gas.
I think the more important restriction (for volumes smaller than the wavelength of sound of a given frequency) is that of the longitudinal friction being negligible. I think all this is well discussed in Landau / Lifshetz Hydrodynamics.

 

[Mapes]

...then you have to explain to me why the adiabatic compression formula is usually used to derive the speed of sound in a gas.
I think the more important restriction (for volumes smaller than the wavelength of sound of a given frequency) is that of the longitudinal friction being negligible. I think all this is well discussed in Landau / Lifshetz Hydrodynamics.

Good point; I was only thinking about one type of system, in which the volume might change via a "bulk" process like a moving piston. In this case, the piston would need to move at much less than the speed of sound to maintain gas equilibrium. But I can see how a compression wave is an entirely different process.