why do air compressor have two stages

No of stages used is governed by the required final pressure. When air is compressed in stages its easier to control the temperature of air. The cooling in intercoolers lowers the work done on compressing. The work saved is evident in the PV diagram, It also has the advantages of less difficulty experienced in lubrication and coking of valves due to the higher air temperature in the single stage compressors. Reason for reduction in work done while compressing in stages. adiabatic compression if air is compressed and heat is not removed(PVɣ= constant), isothermal compression if heat is completely removed(PV=constant).  for compression with inter-cooling, the compression approaches a isothermal compression which is called a polytropic process where (PVn= constant)  since value of n < ɣ the slope of pV diagram is reduced.  {value of ɣ is the ratio of specific heat of air at constant pressure to constant volume} {value of n depends inter cooling is between 1.35 to1.25}