A cooker "A" of 30 cm diameter and volume 30 L is initially filled with liquid water of 4 kg. It is then heated until the pressure in the cooker rises to 5 bar at which pressure it contains a mixture of pure water vapor and liquid water. Then, assume that we insulate the cooker and attach a metal tube of cross sectional area A to it that is placed slightly away from the bottom surface of the cooker. Assume also that we provide a valve at the top of this metal tube. When the valve is opened, the water left in the cooker can be injected into another open adiabatic cooker B of equal dimension in order to conserve energy. We will neglect evaporation from cooker B. However, we would like to monitor the pressure in the first cooker. As an expert in thermodynamics you are asked to predict the pressure vs. time until no liquid water remains. Assume that vapor behaves like an ideal gas with a specific heat of 1.59 kJ/ kg K. Water is incompressible with a specific heat of 4.184 kJ/ kg K and v = 0.001 m3/kg. The cross sectional area of the metal tube is 10 mm2. Assume the power is off when we open the valve and the cooker free space is occupied with vapor only. Neglect the potential energy change.
a) What is the quality when the valve in the metal tube is opened?
b) Write down the mass and energy conservation equations for the vapor phase in the system (assume no condensation of vapor or vaporization of water) and obtain a relation for P vs. v for the vapor phase.
c) What is the quality when all of the water has been expelled from cooker A?
d) Sketch the process for the cooker A on a P-v diagram.
e) Write down the energy balance equation for the metal tube and obtain an expression for velocity through the metal tube assuming that steady state exists for the c.v. (metal tube)
f) Obtain an expression for mass flow through the tube.
g) Derive the expression for P (t) in terms of vapor volume in the cooker?
h) What is the pressure in the cooker when all water is gone?
i) If ln Psat (bar) = 13.09 -4879/T, plot: Tsat vs. t and compare with T vs. t. Check your assumption in (b)