If the room temperature is held at or below 20 degrees celsius (within
a range from 18 to 20) how cool does piped in bottled 99.999% nitrogen
have to be in order to effectively purge all oxygen (given a
volumetric displacement factor of 1) from a container as a result of
becoming heavier than air. At what temperature point does the relative
weight of the two become one, allowing for the heating effect of
surrounding air?

Your question as stated has been approximately answered in the
comments that have already been posted, at least in that the amount of
cooling needed to make pure nitrogen heavier than air (which is 79%
nitrogen anyway). You need only the ideal gas law, n/V = P/RT, to
calculate the density as a function of pressure and temperature.
However, you are really asking at what point you can "effectively
purge all oxygen" from your open container using cold nitrogen as a
purge gas. That is actually a good deal more difficult to determine.
The answer will depend critically on how well you can prevent mixing
of the gas layers and how sensitive you are to residual oxygen
contamination. You don't give your container volume, but a complete
purge in 1.4 seconds will involve gas flow rates high enough to make
turbulent mixing very likely even with a significant difference in gas
density. A detailed system solution would require a lot more
information than you have provided so far, but here are a few
suggestion of directions you could go:

1. Use very cold nitrogen (the vapor from boiling liquid, for example)
if you must use nitrogen.

2. Use carbon dioxide instead. It has a significantly higher density
at room temperature if you cannot tolerate very cold gases.

3. Close your container before you purge (except for a small exit
port) and use several complete air changes of room-temperature
nitrogen.

4. Close your container and consume the oxygen in the container.
Burning most anything is one way to do this, but there are also
materials that absorb oxygen without burning. If you cannot tolerate
sub-atmospheric pressure, you may still need to replace the consumed
oxygen with another gas such as nitrogen.

If you'd like to provide more details on your application (size,
geometry, temperature and pressure constraints, residual oxygen
sensitivity, important time-scales, moving parts [if any], etc.), I
may be able to make some more specific suggestions as to how best to
implement a purge system that will meet your needs. Feel free to
request a clarification if you think a few more qualitative guidelines
will fit your needs, or to post an additional question if you need
more extensive help with a specific system design.

(Answered from personal knowledge of gas dynamics and purging
systems.)

hey tunaboy,

I found the following information at
http://www.allmeasures.com/Formulae/

Density of (dry) air at 25 degrees celsius: 1.225 kg/m^3
Density of oxygen at 25 degrees celsius:    1.429 kg/m^3
Density of nitrogen at 25 degrees celsius:  1.2506 kg/m^3

Unfortunately I cannot locate a density/temperature chart for nitrogen
- but the number for oxygen is probably close enough to what you're
looking for, there shouldn't be a big difference between 25 and 20
degrees.

Regards,
dannidin

dannidin is on the right track. I think the nitrogen only needs to be
about 10 degree c cooler than the air, to be equal density. For gases
like air and nitrogen the density is directly proportional to the
temperature k = kalvin which is the same as c except shifted 273
degees c to absoute zero so 19 degrees c = 292 degrees k.
Unless there is something special about your set up, I think a one
volumn purge of nitrogen will leave at least 1% contaminating oxygen
even if the nitrogen is 20% more dense.  Neil

8.35 degees c cooler than the 19 degree c air = 10.65 degrees c for
the nitrogen might be the correct answer, but that does not allow for
the "heating  effect of  surrounding air" which should be negligible
unless the air is compressed significantly during the purge. The purge
will be poor if the nitrogen mixes with the air. The air will warm the
nitrogen very little if they mix very little. The "heating effect of
surrounding air" will be very little if the nitrogen delivery and
container have thermal insulation.  Neil

I calculated again and got nitrogen 6 degrees cooler than the air in
the container. Sorry if this is not close enough.  Neil

Hey dannidin and neil
Thanks for the info, you guys have been a great help.
The specifics of the setup that I have in relation to your comments -
the air is airconditioned, in an enclosed space, the container is open
to the surrounding air at the time of the nitrogen purge, and remains
so for approximately 1.4 seconds after that time. The nitrogen
pressure is approx. 150 kpa, so I feel it is only slightly higher than
the surrounding air mass, therefore the importance of relative weights
in keeping the nitrogen in an "unmixed" state during the containers
open phase. It is hoped that by finding a point at which it reliably
stays heavier than the surrounding air for the whole of the exposed
period, the nitrogen will not "float off", and thus ensure an
effective purge.
The fact that the surrounding air mass is kept at low temperature
leads me to assume that it also applies a greater than normal pressure
to the overall equation, and I just don't have the necessary research
information to verify this assumption, or a reliable way of
calculating the temperature required for the nitrogen to guarantee
that it will stay within the container for that particular duration.
I am thankful for the help provided, and it sounds as though neil may
have some experience in the field. If you are willing, I would be
happy to discuss this issue further by email if you wish. Although I
must say that I am impressed by the quality of the work done already,
thanks again.