A piston/cylinder setup similar to Problem 3.132 contains 0.1 kg of saturated liquid and vapor water at 100 kPa with quality 25%. The mass of the piston is such that a pressure of 600 kPa will float it. The water is heated to 300°C. Find the final pressure, volume, work 1W2 and heat transfer 1Q2.

a) P₂ = 600 KPa

b) V₂ = 0.043442 m³

c) W₂ = 607.2 KJ

d) Q₂ = 793.39 KJ

Explanation:

Since this is a closed system. Therefore,

m₁ = m₂ = m = 0.1 kg

STATE 1:

Consider the initial state of water. From saturated liquid-vapor mixture table, we have:

Quality = x = 25% = 0.25

Pressure = P₁ = 100 KPa

Specific Volume = v₁ = vf + x(vfg) = 0.001043 m³/kg + (0.25)(1.6930 m³/kg)

v₁ = 0.4243 m³/kg

Specific Internal Energy = u₁ = uf + x(ufg) = 417.4 KJ/kg + (0.25)(2088.2KJ/kg)

u₁ = 939.45 KJ/kg

STATE 1':

Now, the water is heated to state 1' until its pressure becomes 600 KPa to lift the piston. Volume remains constant during this process.

STATE 2:

After reaching a pressure of 600 KPa, the water starts to expand at constant pressure, lifting the piston:

P₂ = 600 KPa

T₂ = 300° C

From property table at 600 KPa, Tsat = 158.83° C

Since, T₂ > Tsat. Therefore, water is in super heated state. From super heated water table:

u₂ = 2801.4 KJ/kg

v₂ = 0.43442 m³/kg

So,

a)

Final Pressure = P₂ = 600 KPa

b)

Final Volume = V₂ = mv₂ = (0.1kg)(0.43442 m³/kg)

V₂ = 0.043442 m³

c)

Work Done = W = P₂ΔV = P₂mΔv = mP₂(v₂ - v₁)

W = (0.1 kg)(600000 Pa)(0.43442 m³/kg - 0.4243 m³/kg)

W = 607.2 KJ

d)

Applying energy eqn. or first law of thermodynamics to the system:

Q₂ = m(u₂ - u₁) + W₂

Q₂ = (0.1 kg)(2801.4 KJ/kg - 939.45 KJ/kg) + 607.2 KJ

Q₂ = 793.39 KJ

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.