A cylinder is fitted with a piston, and the cylinder contains helium gas. The sides of the cylinder are adiabatic, impermeable, and rigid, but the bottom of the cylinder is thermally conductive, permeable to helium, and rigid. Through this permeable wall the system is in contact with a reservoir of constant T and μHe (the chemical potential of He). Calculate the compressibility of the system [−(1/V)(dV/dP)] in terms of the properties of helium (cp, v, α, κT, etc.) and thereby demonstrate that this compressibility diverges. Discuss the physical reason for this divergence.