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