Problem 68
You probably have noticed that balloons inflated with helium gas rise in the air the first day during a party but they fall down the next day and act like ordinary balloons filled with air. This is because the helium in the balloon slowly leaks out through the wall while air leaks in by diffusion. Consider a balloon that is made of \(0.2\)-mm-thick soft rubber and has a diameter of \(15 \mathrm{~cm}\) when inflated. The pressure and temperature inside the balloon are initially \(120 \mathrm{kPa}\) and $25^{\circ} \mathrm{C}$. The permeability of rubber to helium, oxygen, and nitrogen at \(25^{\circ} \mathrm{C}\) are \(9.4 \times 10^{-13}, 7.05 \times 10^{-13}\), and $2.6 \times 10^{-13} \mathrm{kmol} / \mathrm{m} \cdot \mathrm{s} \cdot \mathrm{bar}$, respectively. Determine the initial rates of diffusion of helium, oxygen, and nitrogen through the balloon wall and the mass fraction of helium that escapes the balloon during the first 5 \(\mathrm{h}\), assuming the helium pressure inside the balloon remains nearly constant. Assume air to be 21 percent oxygen and 79 percent nitrogen by mole numbers, and take the room conditions to be \(100 \mathrm{kPa}\) and \(25^{\circ} \mathrm{C}\).
Problem 70
What are the adverse effects of excess moisture on the wood and metal components of a house and the paint on the walls?
Problem 71
How does the condensation or freezing of water vapor in the wall affect the effectiveness of the insulation in the wall? How does the moisture content affect the effective thermal conductivity of soil?
Problem 72
Moisture migration in the walls, floors, and ceilings of buildings is controlled by vapor barriers or vapor retarders. Explain the difference between the two, and discuss which is more suitable for use in the walls of residential buildings.
Problem 73
Why are the insulations on the chilled water lines always wrapped with vapor barrier jackets?
Problem 74
Consider a tank that contains moist air at 3 atm and whose walls are permeable to water vapor. The surrounding air at \(1 \mathrm{~atm}\) pressure also contains some moisture. Is it possible for the water vapor to flow into the tank from surroundings? Explain.
Problem 75
Explain how vapor pressure of the ambient air is determined when the temperature, total pressure, and relative humidity of the air are given.
Problem 76
Express the mass flow rate of water vapor through a wall of thickness \(L\) in terms of the partial pressure of water vapor on both sides of the wall and the permeability of the wall to the water vapor.
Problem 77
A glass of milk left on top of a counter in the kitchen at $15^{\circ} \mathrm{C}, 88 \mathrm{kPa}$, and 50 percent relative humidity is tightly sealed by a sheet of \(0.009\)-mm-thick aluminum foil whose permeance is $2.9 \times 10^{-12} \mathrm{~kg} / \mathrm{s} \cdot \mathrm{m}^{2} \cdot \mathrm{Pa}\(. The inner diameter of the glass is \)12 \mathrm{~cm}$. Assuming the air in the glass to be saturated at all times, determine how much the level of the milk in the glass will recede in \(12 \mathrm{~h}\). Answer: \(0.0011 \mathrm{~mm}\)
Problem 78
Consider a 20 -cm-thick brick wall of a house. The indoor conditions are \(25^{\circ} \mathrm{C}\) and 40 percent relative humidity, while the outside conditions are \(50^{\circ} \mathrm{C}\) and 40 percent relative humidity. Assuming that there is no condensation or freezing within the wall, determine the amount of moisture flowing through a unit surface area of the wall during a 24-h period.
