It is true that gas turbine engines are more efficient than piston engines. This is due to many factors; each part of a jet engine is designed for a specific purpose, the combustion cycle is continuous as opposed to a piston engine whoes cycle is one power stroke for 4 cycles of movement, or 2 in the case of 2 stroke engines.
When I saw this posting I tried to find my BTEC notes (all be it 20 years old) as we covered this subject in some depth to give you some long forgotten facts and figures, but I think they got binned when we moved house. I hope that what I have written is at least a start, and hopefully some bright spark or smart arse will come to our aid!
JFD