Problem # p043

Conservation of Energy, transient

Initial condition :
Mass m1 = 2 kg
Pressure p1 = 200 kPa
Quality x1 = 0.8
Specific volumev1,f = 0.001061 m3/kg
Specific volumev1,g = 0.8857 m3/kg
Internal energy u1,f = 504.49 kJ/kg
Internal energy u1,g = 2529.5 kJ/kg
Enthalpy h1,f = 504.70 kJ/kg
Enthalpy h1,g = 2706.7 kJ/kg

The container above is initially filled with a saturated liquid/vapor mixture of water with data as described in the above table.
Then a crack opens below the water level and liquid water escapes at a rate of 0.02 kg/s. The mass loss lasts for 10 sec at which time the leak is stopped.
  1. What is the mass inside the container after the leak is closed ?
  2. What is the specific volume of the liquid/vapor mixture after the leak is closed ?
  3. What is the internal energy of the liquid/vapor mixture after the leak is closed ? You must use conservation of energy to answer this particular question.
The following simplifications apply :
  1. Potential and kinetic energy effects are negligible.
  2. The container is well-insulated.
  3. The property values of the water leaving the tank remain constant during the leak at a value equal to that corresponding to the initial condition inside the tank.