One way to store a lot of energy is to compress air in a largecave. The air starts at the corner marked by the black dot, where P= 1 atmosphere, V = 1 cave volume (let's choose 1,000,000 cubicmeters), and T = 300 K. It is then adiabatically compressed to halfthe volume by a pump. As the air comes out of the pump it is hotter(how hot? what is the pressure?), but it cools to 300 K again atconstant volume (what is the temperature now?). Later, the airexpands adiabatically running a generator, ending at the initialvolume. It is now colder than 300 K (how cold?) but it warms up toend at the original temperature, pressure, and volume.How much workdid the pump do? How much energy was given to the generator
