Question

Air, modeled as an ideal gas, is compressed at steady state from 1 bar, 300 K, to 5 bar, 500 K, with 170 kW of power input. Heat transfer occurs at a rate of 22.67 kW from the air to cooling water circulating in a water jacket enclosing the compressor. Neglecting kinetic and potential energy effects, determine the mass flow rate of the air, in kg/s.

Answer 1

`\dot m = 0.726\,(kg)/(s)`

Step-by-step explanation:

The process made by the compressor at steady-state is modelled after the First Principle of Thermodynamics:

`-\dot Q_(out) + \dot W_(in) + \dot m \cdot (h_(in) - h_(out)) = 0`

The mass flow rate is:

`\dot m = (\dot Q_(out)-\dot W_(in))/(h_(in)-h_(out))`

For ideal gases, specific enthalpies depends on temperature only. Properties at inlet and outlet are, respectively:

`h_(in) = 300.19\,(kJ)/(kg)`

`h_(out) = 503.02\,(kJ)/(kg)`

The mass flow rate of air is:

`\dot m = (22.67\,kW-170\,kW)/(300.19\,(kJ)/(kg)-503.02\,(kJ)/(kg) )`

`\dot m = 0.726\,(kg)/(s)`