Air, modeled as an ideal gas, is compressed at steady state from 1 bar, 300 K, to 5 bar, 500 K, with 30 kW of power input. Heat transfer occurs at a rate of 4.000 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.

19.56 kg/s

Explanation:

In the given problem, we have:

The temperature and pressure into the system are 300 K and 1 bar respectively. The outlet temperature and pressure are 500 K and 5 bar respectively. The heat transfer rate is 30 kW and the power input is 4000 kW.

If we consider the energy balance equation and neglect both kinetic energy and potential energy, we have:

Thus, the mass flow rate (m) is:

If we use the thermodynamic table for air: ,, , and . Therefore:

m = [-30-(-4000)]/[503.02-300.10] = 3970/202.92 = 19.56 kg/s