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