Question

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?

Answer 1

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.