A pressure cooker is filled with 2.0 kg of liquid water at 30oC. Heat is added to the system, and the relief valve releases saturated water vapor when the pressure reaches 150 kPa. Model the system, and then use the model to plot the amount of heat transfer that occurs as the mass of the water present in the pressure cooker ranges from 1.95 kg to 1.00 kg

Question

State e: outlet state; State 1: Initial State; State 2: Final State.
Given: H2O; m1 = 2.0 kg; T1 = 30oC; P2 = Pe = 150 kPa; xe = 1.0
Assume: As no information is given and these terms are unlikely to be significant, W =
0, and kinetic and potential energy can be neglected. No flow into the system. V =
constant.
What will be an ideal response?

Answer 1

Solution: Using the assumptions, the First Law can be reduced to

2 2 1 1 Q m h m u m u e e ? ? ?

From the conservation of mass, me = m1 – m2

For water: u1 = 125.74 kJ/kg (consider it to be a slightly compressed liquid, with u =

uf@T)

v1 = 0.001004 m3/kg

u2 = [x2 (2052.3) + 466.92] kJ/kg

he = 2610.86 kJ/kg

V = mv1 = 0.002 m3

At state 2, the water is saturated. m2 = mf2 + mg2 : mf2 = m2 – mg2

V = mf2 vf2 + mg2 vg2

vf2 = 0.0010527 m3/kg

vg2 = 1.1594 m3/kg

Substituting: mg2 =

V?m2vf2

vg2?vf2

Then x2 = mg2 / m2

With this known, Q can be found for different amounts of mass present:



In the solution, you may note that the amount of saturated vapor that stays in the tank though half of the mass boiling is very small. It likely can be ignored, with only consideration of a quality of 0 in the tank being needed for reasonable accuracy.