A Tank full of Helium in space?

Classical Mechanics Level 5

A vessel of volume \(\displaystyle V\) containing Helium(\(\displaystyle He\)) is floating in space.

Find the velocity \(\displaystyle v\) (in \(\displaystyle m/s\))at which \(\displaystyle He\) flows out of a small hole in the vessel.

Details and Assumptions:
\(\bullet\) \(\displaystyle He\) is a monoatomic gas.
\(\bullet\) The vessel is thermally insulated.
\(\bullet\) The outside pressure is \(\displaystyle 0 atm\).
\(\bullet\) Velocity inside the vessel is negligible.
\(\bullet\) Temp. of the vessel is \(\displaystyle T = 1000K\)
\(\bullet\) \(\displaystyle V = 1m^3\)


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