A gas flows steadily through a rotary compressor. The gas enters the compressor at a temperature of 16°C, a pressure of 100 kPa, and an
enthalpy of 391.2 kJ/kg. The gas leaves the compressor at a temperature of 245°C, a pressure of 0.6 MPa, and an enthalpy of 534.5 kJ/kg. There is no heat transfer to or from the gas as it flows through the compressor.
(a) Evaluate the external work done per unit mass of gas assuming the
gas velocities at entry and exit to be negligible.
(b) Evaluate the external work done per unit mass of gas when the gas
velocity at entry is 80 m/s and that at exit is 160 m/s.
Answers
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Answer:
(a) The external work done per unit mass of gas is 143.3 kJ/kg.
(b) The external work done per unit mass of gas is 152.3 kJ/kg.
Explanation:
From the above question,
They have given :
External work is defined as the energy required to move a unit mass of gas from one point to another. The external work done per unit mass of gas is equal to the enthalpy change between the two points. Thus, the external work done per unit mass of gas can be calculated as the difference between the enthalpy of the gas at the entry and exit points, divided by the mass of the gas.
step by step
(a) The external work done per unit mass of gas can be calculated as follows:
External work done per unit mass of gas = (Enthalpy at exit - Enthalpy at entry) / Mass of gas
= (534.5 - 391.2) kJ/kg / 1 kg
= 143.3 kJ/kg
(b) The external work done per unit mass of gas can be calculated as follows:
External work done per unit mass of gas = (Enthalpy at exit + Kinetic Energy at exit - Enthalpy at entry - Kinetic Energy at entry) / Mass of gas
= (534.5 + 0.5*(160^2 - 80^2) - 391.2 - 0.5*(80^2)) kJ/kg / 1 kg
= 152.3 kJ/kg
(a) The external work done per unit mass of gas is 143.3 kJ/kg.
(b) The external work done per unit mass of gas is 152.3 kJ/kg.
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