In article <q1TiuB3w165w@inqmind.bison.mb.ca> norm@inqmind.bison.mb.ca (Norman P. Paterson) writes:
>I'VE TOYED WITH THE PV=NRT FORMULA FOR GASES. I'M DESIGNING A SMALL
>AIRHSIP AND WISH TO CALCULATE THE EXPANSION OF THE HELIUM. YOU COULD
>REALLY HELP ME OUT IF YOU COULD TELL ME HOW TO USE THIS FORMULA PROPERLY.
>I'D LIKE TO GIVE A PRACTIAL EXAMPLE AND PERHAPS YOU COULD EXPLAIN TO
>MYSELF HOW TO APPLY THIS FORMULA TO THE PROBLEM (OR ANY OTHER PERTINENT
>FORMULA).
>- Take a aluminium ball with a voulume of 100 cu/meters. Say that this
>ball is indestructible. The ball is filled with helium gas on the ground
>(the gas is 99.9% pure). Now, take this ball to an alititude of 100,000
>feet. What would the internal pressure be of the ball (or helium)?
>
>
>Well, thanks!
>Norman Paterson
>Wpg MB CANADA
>
>norm@inqmind.bison.mb.ca
>The Inquiring Mind BBS, Winnipeg, Manitoba 204 488-1607
First, PV=nRT is what is often called the ideal gas relation, or equation of
state. As such it is only good for gasses, and as its name implies, it is
only an idealization (although for helium at near atmospheric conditions, it is
usually quite good).
"n" is the number of moles of the gas, R is the universal gas constant (8.31441
kJ/(kmol K), T is absolute temperature, P is absolute pressure, and V is volume.
The way this equation is most often used is to calculate any of the above
variables (except R, of course) in terms of the others.
For your example, since there is not enough information to assume otherwise, I
will make the assumption that the ball is perfectly rigid, and does not deform
under changing pressures. If the ball is filled at sea level, then the
internal pressure is one atmosphere (14.7 psi), and if the temperature stays
constant at 100,000 ft, then T is constant, R is defined constant, since the
ball does not expand or contract, V is constant, and if no gas is added or
removed then n is constant, and hence P=nRT/V is constant.
In reality, the temperature of the atmosphere changes with altitude, and if we
assume that the gas in the ball is the same temperature as the surrounding air,
we can find the internal pressure. From a table of the U.S. Standard Atmosphere we see that the temperature (a time average over the U.S.) at 100,000 ft is
about 227 K.
How many moles of gas did you start with? From PV=nRT, we find that you have
about 4100 moles (I am rounding my numbers). At altitude, again using the
ideal gas relation, the internal pressure is about 7.7*10^4 Pa, or 11 psi.
The atmospheric pressure at this altitude is about 0.17 psi.
I am not sure why you want to know the internal pressure, since helium balloon
will expand with altitude (especially if it is your typical sort of weather-
balloon),but unless you are really interested in the stresses in a more rigid
material like aluminum, you maybe would be more interested in the bouyancy
