Minimal container.

Let the mass of the given ideal gas be " m " ,

the molecular mass of the given ideal gas be " M " ,

the mass density per unit volume of the container be " ρ " ,

the tensile strength of the container material be " σ " ,

the radius of the container be " r " ,

the temperature maintained inside the container be " T " .

Let us calculate the pressure exerted by the given ideal gas , which I am going to take as " P " .

P . 43 Ï€ r ³ = mM R T

Or , P = 3 m R T4 Ï€ r ³ M

For the container to sustain this pressure , we must have : -

P . Ï€ r ² < σ . 4 Ï€ r ²

Or , P < 4 σ

Or , 3 m R T4 Ï€ r ³ M < 4 σ

Or , m R T4 σ M < 43 Ï€ r ³

Now , the weight of the container = 43 Ï€ r ³ ρ g

Hence , the minimal weight of the container , W = m ρ R T g4 σ M

Note : - I think this value of " W " is not achievable .