Serway & Jewett — Temperature: Problem 46

Helium gas is sold in steel tanks that will rupture if subjected to tensile stress greater than its yield strength of \(5 \times 10^8 \text{ N/m}^2\). If the helium is used to inflate a balloon, could the balloon lift the spherical tank the helium came in? Justify your answer. Suggestion: You may consider a spherical steel shell of radius \(r\) and thickness \(t\) having the density of iron and on the verge of breaking apart into two hemispheres because it contains helium at high pressure.