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As the pressure ratio increases in an ideal turbojet (fixed flight Mach number), the specific thrust, $\frac{F}{\dot{m_{air}}}$ rises, reaches a peak for small pressure ratios and then starts to decrease with increasing pressure ratios in the compressor.

It seems counter-intuitive to assume that the specific thrust should decrease with increasing compressor pressure ratio since we're generating a greater pressure gradient, therefore should be able to generate more thrust.

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Increased compressor pressure ratio means increased temperature in inlet of the turbine.
Turbine has limits $T_{max}$ on inlet temperature (turbine could melt). To keep temperature in operational limits the fuel/air mass ratio $f$ is lowered at high pressure ratios.

Lowered fuel/air mass ratio $f$ means that less chemical energy is released per mass unit of the air.

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follow up: Do you know why specific fuel consumption has a minimum if losses are considered? –  l3win Nov 20 '13 at 6:05

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