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The compressor of a gas turbine plant, operating on an ideal intercooled Brayton cycle, accomplishes an overall compression ratio of $6$ in a two-stage compression process. Intercooling is used to cool the air coming out from the first stage to the inlet temperature of the first stage, before its entry to the second stage. Air enters the compressor at $300\: K$ and $100\: kPa$. If the properties of gas are constant, the intercooling pressure for minimum compressor work is __________ $kPa$ (rounded off to $2$ decimal places).
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