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In a steady–flow compressor, $40\ kmol$ per hour of a gas at $1.0\ bar$ and $300\ K$ with a velocity of $10\ m / s$ is compressed to $6.0\ bar$ and $500\ K$ with a velocity of $4.0\ m / s$. Assume for the gas that enthalpy is independent of pressure and that the constant–pressure heat capacity is $(7 / 2) R$ with $R = 8.314\ J / mol \cdot K$. What is the rate of heat transfer from the compressor if the delivered mechanical power is $100.0\ kW$?