When air is compressed, the enthalpy is increases from 100 KJ/kg to 200 KJ/Kg. Heat lost during this compression is 50 KJ/kg. Neglecting Potential and Kinetic energies, the power required for a mass flow of 2 kg/sec of air through compressor will be

Concept:​

\({h_1} + \frac{{V_1^2}}{2} + {z_1}g + \frac{{dQ}}{{dm}} = {h_2} + \frac{{V_2^2}}{2} + {z_2}g + \frac{{dW}}{{dm}}\;\;\;\;(1)\)

Eq (1) is the Steady flow energy equation in mass form.

\(\dot{m_1}({h_1} + \frac{{V_1^2}}{2} + {z_1}g) + \dot{Q} = \dot{m_2}\left( {{h_2} + \frac{{V_2^2}}{2} + {z_2}g} \right) + \dot{W}\;\;\;\;\;(2)\)

Eq (1) is the Steady flow energy equation in mass form.

Calculation:

Given:

ṁ = 2 kg/s, h1 = 100 kJ/kg, h2 = 200 kJ/kg, Q̇ = -50 KJ/kg, (KE & PE Negalected)

\({h_1} + \frac{{V_1^2}}{2} + {z_1}g + \frac{{dQ}}{{dm}} = {h_2} + \frac{{V_2^2}}{2} + {z_2}g + \frac{{dW}}{{dm}}\;\;\;\;\)

\( \dot{W}=\dot{m_1}({h_1} -{h_2})+\dot{m} \left(\ \dot{Q}\right) \)

Ẇ = 2 × (100-200) + 2 × (-50) ⇒ -300 kW(-ve sign indicates that work consumed by the system)