This infor should be enough. make assumptions if needed.

Consider a sand$-$based thermal energy storage system used for storing electrical energy. Electrical energy is stored in the system using heating elements, causing the sand's temperature to rise during charging. The storage system is assumed to be lossless.

The thermal energy stored in the system is intended to be converted back into electrical energy using a gas turbine system. The thermal storage system is designed to replace the combustion chamber of the gas turbine. Air is pressurized in a compressor, receives heat from the thermal storage system, and expands in the turbine.

Calculate the required temperature of the storage system for the gas turbine$$s instantaneous process efficiency to be $20\%.$ Determine the amount of energy needed to charge the storage system to reach this temperature. Also, calculate the electrical power output of the gas turbine system at the storage system's maximum temperature.

Draw an indicative diagram showing what happens to the gas turbine system's process efficiency as the thermal storage system is discharged. Additionally, describe scenarios where such a combination of thermal storage and a gas turbine could be economically viable and how the setup could be improved.

Thermal Storage ParametersValueUnitHeight of the storage system$6$mDiameter of the storage system $($cylindrical$)3$mSand density$1800$kg$/$m$^3$Sand heat capacity$2100$J$/$kg$$KInitial temperature of the storage system$400$K

Initial Values for the Gas Turbine SystemValueUnitAir mass flow rate$10$kg$/$sRuR$\_$uRu$($Universal gas constant$)8\mathrm{.}314$J$/$mol$$KMolar mass of air$0\mathrm{.}028965$kg$/$molPressure ratio$10-$Air inlet temperature$280$KCompression efficiency$0\mathrm{.}8-$Expansion efficiency$0\mathrm{.}9-$Gas turbine system efficiency$0\mathrm{.}200-$