## PSN-L Email List Message

Subject: Re: BBC news article about infrasound
From: ChrisAtUpw@.......
Date: Mon, 17 Feb 2003 08:56:11 EST

```In a message dated 17/02/03, hernlund@............ writes:

> Hey Chris,
>     In the ideal gas treatment (this is where the approximate comes in),
> the equation of state is just PV=nkT where P is pressure, V is volume, n is
> number of molecules, k is Boltzman's constant, and T is temperature. This
> is the same as P=rkT where r is the number density. While this is quite
> approximate, it does capture the gross features of the atmosphere
> surprisingly well. The hydrostatic part of the atmospheric equilibrium
> (force balance) is determined by dP/dz
> proportional to -r*g, where g is the gravitational acceleration. At
> constant T this gives you: dP/dz proportional to -P*g/kT or upon
> integrating just P proportional
> to exp(-z*g/kT) where z is the height. Since P is proportional to r in this
>

Hi John,

This seems to be a rather convoluted and confusing way of expressing a
simple velocity.

I haven't a clue what a number density is supposed to represent. Would
you care to define it please?

It is quite easy to show that the velocity of sound in a gas is given
by c = Sqrt(gamma x P / rho), where gamma is the ratio of the specific heats,
P is the pressure and rho is the density = mass / volume V. Hence PV ---> RT
and you don't have to bother with P and V.

Putting in the equation of state gives c = Sqrt(gamma x R x T / M),
where R is the gas constant, T is the temperature and M is the molecular
weight. None of these is a function of another and the expression should be
roughly correct at all pressures until the mean free path effects /
ionisation etc become dominant factors. See Kaye and Laby, Tables of Physical
and Chemical Constants.

Regards,

Chris Chapman
In a message dated 17/02/=
03, hernlund@............ writes:

Hey Chris,
In the ideal gas treatment (this is where the approxi=
mate comes in), the equation of state is just PV=3DnkT where P is pressure,=20=
V is volume, n is number of molecules, k is Boltzman's constant, and T is te=
mperature. This is the same as P=3DrkT where r is the number density. While=20=
this is quite approximate, it does capture the gross features of the atmosph=
ere surprisingly well. The hydrostatic part of the atmospheric equilibrium (=
force balance) is determined by dP/dz=20
proportional to -r*g, where g is the gravitational acceleration. At cons=
tant T this gives you: dP/dz proportional to -P*g/kT or upon integrating jus=
t P proportional=20
to exp(-z*g/kT) where z is the height. Since P is proportional to r in t=
his case, then density also falls off exponentially with height.

Hi John,

This seems to be a rather convolute=
d and confusing way of expressing a simple velocity.

I haven't a clue what a number dens=
ity is supposed to represent. Would you care to define it please?

It is quite easy to show that the v=
elocity of sound in a gas is given by c =3D Sqrt(gamma x P / rho), where gam=
ma is the ratio of the specific heats, P is the pressure and rho is the dens=
ity =3D mass / volume V. Hence PV ---> RT and you don't have to bother wi=
th P and V.

Putting in the equation of state gi=
ves c =3D Sqrt(gamma x R x T / M), where R is the gas constant, T is the tem=
perature and M is the molecular weight. None of these is a function of anoth=
er and the expression should be roughly correct at all pressures until the m=
ean free path effects / ionisation etc become dominant factors. See Kaye and=
Laby, Tables of Physical and Chemical Constants.=20

Regards,

Chris Chapman
```