A 30 m3 steam boiler contains a mixture of liquid water and water vapor at 700 kPa. Initially the vapor and liquid occupy equal volumes. A valve is opened to withdraw the vapor and simultaneously another valve is opened to add liquid water. During some time interval, 15,000 kg of 40°C liquid are added to the boiler, while the vapor is being withdrawn. During this whole process the pressure inside the boiler is maintained at 700 kPa. At the end of the process the liquid water remaining in the tank occupies ¼ of the boiler volume, with vapor filling the rest. Potential and kinetic energy impacts are negligible in this process.
a. (5 points) What is the temperature in the boiler before the valves are opened?
b. (10 points) How much vapor is withdrawn during the whole process (in kg)?
c. (10 points) Fill in the values in the schematic below.
d. (25 points) How much heat was transferred to the boiler during this process?
My answers:
a. Liquid water and water vapor mixture => table 5.2: P=700 kPa; T=164.94
b. P=700 Kpa => Vl = 0.001108 m3/kg; Vv = 0.27286 m3/kg
T=40 C => Vl=0.001008 m3/kg
V(bar)1 = (1-x)Vl+xVv=0.5*0.001108+0.5*0.27286 = 0.1370 m3/kg => m1=V/V(bar)1 = 30/0.1370 = 219 (kg)
V(bar)2 = (1-x)Vl+x*Vv = 0.25*0.001108 +0.75*0.27286 = 0.2049 m3/kg => m2=V/V(bar)2=30/0.2049=146 (kg)
m2 = m1+m(liquid add)-m(vapor out) = 219 + 15000-146 = 15073 (kg)