Question

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.

Answer 1

Answer:

19.56 kg/s

Explanation:

In the given problem, we have:

The temperature $(T_{1})$ and pressure into the system are 300 K and 1 bar respectively. The outlet temperature $(T_{2})$ and pressure $(p_{2})$ are 500 K and 5 bar respectively. The heat transfer rate $(Q_{cv})$ is 30 kW and the power input $(W_{cv})$ is 4000 kW.

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

$0 =Q_{cv} - W_{cv} + m(h_{1}-h_{2})$

Thus, the mass flow rate (m) is:

$m = \frac{Q_{cv}-W_{cv}}{h_{2}-h_{1}}}$

If we use the thermodynamic table for air: $h_{2} = 503.02 kJ/kg$,$h_{1} = 300.10 kJ/kg$, $Q_{cv} = - 30kW$, and $W_{cv} = -4000 kW$. Therefore:

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