1/ Power an air compressor with 13.38 kWh of electric energy to produce heating for a household's daily hot water consumption. The electric energy is converted to heat energy at about 60°C to produce 270 litres of hot water at 55°C and compressed air cooled to 25°C and 8 atmospheres.
See the spreadsheet below for calculations of thermal energy needed to supply 270 litres of hot water per day for a household or business.
2/ The compressed air produced at 25°C and 8 atmospheres (absolute) pressure may be used for driving compressed-air tools.
See the spreadsheet "AirCompressor" for the calculation of the energy used by the compressor and the volume of air it compresses.
3/ The compressed air instead may be used in a solar-air turbine to deliver 24.55 kWh at 100% thermal efficiency by compressing it adiabatically to 32 atmospheres before heating it further with an external thermal energy source at constant pressure then expanding it adiabatically before finally outputting it at 25°C and 1 atmosphere pressure.
See the spreadsheet "AirHeatEngine" for the calculation of the conversion of heat energy to 24.55 kWh electrical energy at 100% conversion efficiency with the compressed air that was produced while providing a household or businesses daily hot water requirements.
Note that while the conversion of thermal energy to electrical energy can achieve an efficiency of 100%, the total efficiency takes into account the 13.38 kWh consumed to produce the compressed air. The overall efficiency for this model is (24.55 - 13.38) / 24.55 = 45.5%.