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In a simple Brayton cycle, the pressure ratio is $8$ and temperatures at the entrance of compressor and turbine are $300$ $K$ and $1400$ $K$, respectively. Both compressor and gas turbine have isentropic efficiencies equal to $0.8$. For the gas, assume a constant value of $c_p$ (specific heat at constant pressure) equal to $1$ $kJ$/$kgK$ and ratio of specific heats as $1.4$. Neglect changes in kinetic and potential energies.

The power required by the compressor in $kW$/$kg$ of gas flow rate is

  1. $194.7$
  2. $243.4$
  3. $304.3$
  4. $378.5$
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