# Why does the specific thrust of an ideal turbojet drop with increasing compressor pressure ratio?

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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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.