Energy storage is necessary to, for example, allow solar-derived electricity to be generated around the clock. For a given mass of storage medium, show that the ratio of sensible thermal energy storage capacity to potential energy storage capacity may be expressed as

\[R=\frac{\Delta E_{\mathrm{st}, t}}{\Delta E_{\mathrm{st}, \mathrm{PE}}}=\frac{c \Delta T}{g z}\]

where \(\Delta T\) is the difference between the maximum and minimum temperatures associated with thermal energy storage, \(c\) is the specific heat, and \(z\) is the vertical coordinate for potential energy storage. Considering stone mix concrete as the storage medium, determine the value of \(R\) for \(\Delta T=100^{\circ} \mathrm{C}\) and \(z=100 \mathrm{~m}\). Which energy storage approach, thermal or potential, is more effective for the parameters of this problem?