372 a the air in the air inlet 372 a may have a temperature of e g 20 celsius degrees and a pressure of e g 1 bar during compression of the air the pressure may rise to e g 25 bar and the temperature may rise to e g 500 celsius degrees this heated up and compressed air is fed into an inlet of a heat exchanger arrangement 310 of the thermal energy storage and recovery device 300 the compressed air then returns via an outlet of the heat exchanger arrangement 310 now having a temperature of e g 20 celsius degrees and a pressure of still nearly 25 bar the compressed outlet air is then fed into an air turbine 374 according to the embodiment described here the air turbine 374 and the motor 376 and the compressor 372 have a common shaft 377 this provides the advantage that the air turbine 374 will help the motor 376 driving the compressor 372 such that the efficiency of the heat generating arrangement 370 will be increased the temperature of expanded outlet air being provided by the air turbine 374 via an air outlet 374 a may e g fall to minus one degrees celsius u2212 1 u00b0 c when the air is expanded from a pressure of 25 bar to 1 bar this makes the expanded outlet air from the air turbine 374 suitable for cooling purposes e g for air conditioning of the surrounding air in one or more rooms in one or more buildings to recover stored energy a cold fluid.