The reciprocating piston compressor

If during the compression of unit mass of gas, its volume changes by an amount du at a pressure P, the net work done on the gas, —5W, for a reversible change is given by  

The work done in a reversible compression will be considered first because this refers to the ideal condition for which the work of compression is a minimum a reversible compression would have to be carried out at an infinitesimal rate and therefore is not relevant in practice. The actual work done will be greater than that calculated, not only because of irreversibility, but also because of frictional loss and leakage in the compressor. These two factors are difficult to separate and will therefore be allowed for in the overall efficiency of the machine. 

The total work of compression from a pressure Pi to a pressure P2 is found by integrating equation 8.27. For an ideal gas undergoing an isothermal compression  

Under these conditions the whole of the energy of compression appears as heat in the gas. For unit mass of an ideal gas undergoing an isentropic compression  

Eliminating and V2 gives the ratio of the outlet temperature 7 2 to the inlet temperatures T ]  

---