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

Answer:

$\dot m = 0.726\,\frac{kg}{s}$

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:

$\dot m = \frac{\dot Q_{out}-\dot W_{in}}{h_{in}-h_{out}}$

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

$h_{in} = 300.19\,\frac{kJ}{kg}$

$h_{out} = 503.02\,\frac{kJ}{kg}$

The mass flow rate of air is:

$\dot m = \frac{22.67\,kW-170\,kW}{300.19\,\frac{kJ}{kg}-503.02\,\frac{kJ}{kg} }$

$\dot m = 0.726\,\frac{kg}{s}$