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

19.56 kg/s

Step-by-step 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 = (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