Water is placed on a stove to boil in a container that has a flexible lid so that it can expand with increasing amounts of water vapor while not losing any water to the surroundings. The mass of the water is 2 kg. Initially, the water is a saturated liquid at 100oC, and the boiling process is at constant pressure. 10 kW of heat is added to the water, and the process continues until ¾ of the water has become water vapor

Question

(a) Determine the time elapsed for the process.
(b) Develop a computer model to simulate this problem, and plot the net heat transfer, the net work done and the quality of the water all as a function of time. Consider the time to start as 25 s, and to end when the boiling process is complete (i.e., when the water is a saturated vapor.)
Given: Water; m = 2 kg; T1 = 100oC; x1 = 0; P = constant; Q?=10 kW; x2 = 0.75
Assume: ?KE = ?PE = 0

What will be an ideal response?

Answer 1

Solution: (a) The First Law for a closed system reduces to

Q – W = m (u2 – u1)

For the states given, u1 = 418.99 kJ/kg; u2 = 1984.26 kJ/kg

P = Psat = 101.325 kPa

The moving boundary work can be found from

W = P (V2 – V1) = mP(v2 – v1)

v1 = 0.001043 m3/kg

v2 = 1.254 m3/kg

So, W = 254 kJ

Q = m (u2 – u1) + W = 3385 kJ

The time elapsed is t = Q/Q? = 338.5 s = 5.64 min



(b) Note that the heat transfer is also equal to the change in enthalpy for this constant-pressure process: Q = m (h2 – h1). Therefore, the model can be set up to solve for the enthalpy at different times, which can be used to find the quality, then the specific volume, and then the work: