Final answer:
The problem requires using the steady-flow energy equation to calculate the power developed and the volumetric flow rate at the inlet for air passing through a device. We use the first law of thermodynamics, specific heat capacity at constant pressure, and the ideal gas law to find the mass flow rate, and then the power and inlet volumetric flow rate.
Step-by-step explanation:
The problem involves applying the first law of thermodynamics to a control volume through which air is flowing steadily. Considering that air behaves as an ideal gas with constant specific heats, we can calculate the power developed and the volumetric flow rate at the inlet. Given that the process neglects kinetic and potential energy effects, we use the steady-flow energy equation:
Q = m ⋅ c_p ⋅ ΔT
Where Q is the rate of heat transfer (347 kJ/kg), m is the mass flow rate, c_p is the specific heat at constant pressure (1.04 kJ/kg.K), and ΔT is the change in temperature.
The mass flow rate can be calculated from:
m = ρ ⋅ V
Where ρ is the density of air (which can be found from the ideal gas equation, ρ = P/RT), and V is the volumetric flow rate of air exiting the device (1.8 m³/s).
After calculating the mass flow rate, we can find:
- The power developed using the relation P = m ⋅ Δh, where Δh (change in enthalpy) can be found from Δh = c_p ⋅ ΔT.
- The volumetric flow rate at the inlet using the continuity equation V_in = ρ_in ⋅ V_exit / ρ_exit.
Given that the air is exiting at 1 bar and 500 K, we can use the ideal gas law to find density at the exit, and then use the exit conditions to find the volumetric flow rate at the inlet.