Superheated steam, at a mass flow rate of 15.0 kg/s, enters an insulated mixing chamber at 500 kPa and 200°C. In the chamber, the steam is mixed with liquid water at 500 kPa and 40°C. Determine the mass flow rate of the entering liquid water required for the combined flow to exit as a saturated liquid at 500 kPa.
State 1: Steam inlet; State 2: Water inlet; State 3: Outlet
Given: T1 = 200°C; P1 = P2 = P3 = 500 kPa; m?1= 15.0 kg/s; T2 = 40°C; x3 = 0.0
Assume: Q?=0 (insulated). Also, given no other information regarding the mixing chamber, make the following common assumptions: W?=?KE=?PE=0
Also, assume the mixing chamber is a multiple-inlet, single-outlet, steady-state, steady-flow device.
What will be an ideal response?
The First Law for Open Systems reduces to m?1h1+m?2h2=m?3h3
The conservation of mass yields: m?1+m?2=m?3
For water:
h1 = 2855.4 kJ/kg
h2 = 167.57 kJ/kg (Consider this a slightly compressed liquid, and just use hf @ T2)
h3 = 640.23 kJ/kg
Combining the First Law and the conservation of mass:
m?2=m?1(h3?h1)/h2?h3 = 70.3 kg/s
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