(a) Almost all equations of state satisfy the condition (∂²V/∂P²)_s > 0. Show that, when this condition is satisfied, the Rankine-Hugoniot relations and the law of entropy increase imply that the pressure and density must increase across a shock and the fluid must decelerate: P₂ > P₁, V₂ < V₁, and v₂ < v₁.

(b) Show that in a fluid that violates (∂²V/∂P²)_s > 0, the pressure and density must still increase and the fluid decelerate across a shock, as otherwise the shock would be unstable.