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Carbon dioxide is being compressed from 100 kPa and 300 K to 600 kPa and 500 K. The compressor has a flowrate of 1.5 kg/s and heat is being lost from the compressor at a rate of 50 kW. What is the rate of shaft work, in kW, consumed by this compressor?

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Answer:429.8 KW

Explanation:

carbon dioxide Inlet temperature
300K and pressure 100 KPa

At given Temperature and presssure
c_p_1=0.846 kJ/kg-k

Flow rate
\dot{m} =1.5 kg/s

Steam Outlet temperature and Pressure is
500K and pressure is 600 KPa


c_p_2=1.014 kJ/kg-k

Heat loss 50 KW

Applying Steady Flow Energy Equation


\dot{m}\left ( h_1+(v_1^2)/(2)+z_1 \right )+\dot{Q}=\dot{m}\left ( h_2+(v_2^2)/(2)+z_2 \right )+\dot{W}

Neglecting Kinetic and Potential Energy changes


\dot{m}h_1+\dot{Q}=\dot{m}h_2+\dot{W}


\dot{W}=\dot{m}\left ( c_p_1T_1-c_p_2T_2\right )+\dot{Q}


\dot{W}=1.5\left ( 0.846* 300-1.014* 500\right )-50


\dot{W}=429.8 KW

Negative sign indicates work is being done on the system.

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