I have a question about vapor expansion in an open field? (not for school)?

Question

If 50L of liquid nitrogen in a Dewer was very rapidly to convert to gas (it would form a vapor cloud of this), how big would the cloud be?

I know that 1 liquid Nitrogen will expand to produce about 696.5 equivalent volumes of gas, but I can't figure out how large that initial could would be, mainy because it can't expand down so it is not going in that direction and would have to go up and to the sides only.

So I guess what I am asking is this: how wide would the 'cloud radius' around the dewar be, and how tall would the cloud be.

I will give best answer to someone who can help me visualize this. Thanks!

Answer 1

You already know that your 50 L of LN2 will expand to about ( 7000 ) ( 50 ) = 350,000 L or 350 m³. You know the gas will expand up and out, so consider the volume of a hemisphere:

( 1/2 ) ( 4/3 ) π r³

The resulting radius is about 5.5 meters.