QJB had another question:
why is it that both the piston engine and the turbine engine can have their efficiencies increased by increasing the pressure ratio (compression ratio for piston)?
The mathematics behind all this is quite complex, but it all hinges around Carnot's theorem
Carnot's theorem (thermodynamics) - Wikipedia, the free encyclopedia
No engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between the same reservoirs.
The maximum efficiency is 1-T_H/T_C
Ref:
Thermal efficiency - Wikipedia, the free encyclopedia
For a gas turbine this translates to 1-(P2/p1)^(1-y/y) with y the adiabatic index (~7/5 for air)
A turbo charger can add to the efficiency of a Diesel engine, but not to that of a petrol (Otto) engine, as the compression is limited by self combustion of the mixture. A turbo charger allows to obtain more power from a smaller engine too.