No, you are right. In the long run, the number of CO2 molecules left in the bottle when you close it is all that matters. Those molecules will drift in and out of the liquid and gas phases until they reach equilibrium. At the equilibrium point, there will be enough molecules in the gas phase to pressurize the bottle and enough in the liquid phase to give the beverage a reasonable amount of bite.
By giving the sealed bottle a shake, your mother-in-law is simply speeding up the approach to equilibrium. She is helping the CO2 molecules leave the beverage and enter the gas phase. The bottle then pressurizes faster, but at the expense of dissolved molecules in the beverage itself. If there is any chance that you'll drink more before equilibrium has been reached, you do best not to shake the bottle. That way, the equilibration process will be delayed as much as possible and you may still be able to drink a few more of those CO2 molecules rather than breathing them.
Incidentally, shaking a new bottle of soda just before you open it also speeds up the equilibration process. For an open bottle, equilibrium is reached when essentially all the CO2 molecules have left and are in the gas phase (since the gas phase extends over the whole atmosphere). That's not what you want at all. Instead, you try not to shake the beverage so that it stays away from equilibrium (and flatness) as long as possible. For most opened beverages, equilibrium is not a tasty situation.
As the snow settles and becomes denser, it may feel "heavier", but its total weight doesn't change much. The same water molecules are simply packing themselves into a smaller space. So while each shovel-full of the dense stuff really does weigh more than a shovel-full of the light stuff, the total number of water molecules present on your deck and their associated weight is still the same.
In actually, some of the water molecules have almost certainly left via a form of solid-to-gas evaporation known technically as "sublimation." You have seen this conversion of ice into gas when you have noticed that old ice cubes in your freezer are smaller than they used to be or when you see that the snow outside during a cold spell seems to vanish gradually without ever melting. Sublimation is also the cause of "freezer burn" for frozen foods left without proper wrapping.
Despite the freezer's low temperature and the motionlessness of all the frozen foods inside it, there is still plenty of microscopic motion going on. Every surface inside the freezer is active, with individual molecules landing and leaving all the time. Whenever a molecule on the surface of a piece of food manages to gather enough thermal energy from its neighbors, it will break free of the surface and zip off into the air as a vapor molecule. And whenever a vapor molecule in the air collides with the surface of another piece of food, it may stick to that surface and remain there indefinitely.
Since the freezer has a nearly airtight seal, the air it contains remains inside it for a long time. That means that the odor molecules that occasionally break free of a pungent casserole at one end of the freezer have every opportunity to land on and stick to an ice cube at the other end. With time, the ice cube acquires the scent of the casserole and becomes unappealing.
To stop this migration of molecules, you should seal each item in the freezer in its own container. That way, any molecules that leave the food's surface will eventually return to it. Since ice cubes are normally exposed to the air in the freezer, keeping the odor molecules trapped in their own sealed containers keeps the freezer air fresh and the ice cubes odor-free.
What thrills me about your question is that while we've all noticed this effect, we're never taught why it happens. Let me ask your question in another way: we know that opening a window makes the clothes dry faster, but how do the clothes know that the window is open? Who tells them?
The explanation is both simple and interesting: the rate at which water molecules leave the cloths doesn't depend on whether the window is open or closed, but the rate at which water molecules return to the cloths certainly does. That return rate depends on the air's moisture content and can range from zero in dry air to extremely fast in damp air. Air's moisture content is usually characterized by its relative humidity, with 100% relative humidity meaning that air's water molecules land on surfaces exactly as fast as water molecules in liquid water leave its surface. When you expose a glass of water to air at 100% relative humidity, the glass will neither lose nor gain water molecules because the rates at which water molecules leave the water and land on the water are equal. Below 100% relative humidity, the glass will gradually empty due to evaporation because leaving will outpace landing. Above 100% relative humidity, the glass will gradually fill due to condensation because landing will outpace leaving.
The same story holds true for wet clothes. The higher the air's relative humidity, the harder it becomes for water to evaporate from the cloths. Landing is just too frequent in the humid air. At 100% relative humidity the clothes won't dry at all, and above 100% relative humidity they'll actually become damper with time.
When you dry clothes in a room with the window open and the relative humidity of the outdoor air is less than 100%, water molecules will leave the clothes more often than they'll return, so the clothes will dry. But when the window is closed, the leaving water molecules will remain trapped in the room and will gradually increase the room air's relative humidity. The drying process will slow down as the water-molecule return rate increases. When the room air's relative humidity reaches 100%, drying will cease altogether.
During wine making, the amount of dissolved carbon dioxide (and possibly oxygen gas) can easily exceed its equilibrium concentration. That means that the liquid contains more dissolved gas than it would have if exposed to the atmosphere for a long period of time and had thereby reached its equilibrium concentration of the gas. Having too much dissolved gas does not, however, mean that this gas will leave quickly. For example, when you open a bottle of carbonated beverage the carbon dioxide is out of equilibrium. Although the gas was in equilibrium at the high pressure of the sealed bottle, it instantly became out of equilibrium when the bottle was opened and the density of gaseous carbon dioxide suddenly decreased. Nonetheless, it can take days for the excess carbon dioxide to come out of solution and leave. You've probably noticed that carbonated beverages take hours or days to "go flat."
Part of the reason why it takes so long for the dissolved gases to come out of solution is that the gas can only leave through the exposed surface of the liquid. In an open bottle of carbonated beverage that may be only a few square inches or a few dozen square centimeters. The dissolved gas has to find its way to that exposed surface and break free of the liquid. That's a slow process. The same thing is happening in your wine: the dissolve carbon dioxide and oxygen gases must normally find their way to the top of the tank and then break free to enter the gaseous region at the top of the tank another slow processes. To speed the escape of dissolved gases, you can enlarge the exposed surface of the liquid by bubbling an inert gas through the liquid. Here, inert gas is any gas that doesn't dissolve significantly in the liquid and that doesn't affect the liquid if it does dissolve. Nitrogen is great for wine because it doesn't interact chemically with the wine. As you let bubbles of nitrogen float upward through the wine, you provide exposed surface within the body of the liquid wine and allow carbon dioxide and oxygen to break free of the liquid and enter those bubbles.
The spherical interface between the gas bubble and the surrounding liquid is a busy, active place gas molecules are moving between the gas and liquid in both directions. Because carbon dioxide is over-concentrated in the liquid, it is statistically more likely for a carbon dioxide molecule to leave the liquid and enter the bubble's gas than the other way around. It takes a little energy to break those carbon dioxide molecules free of the liquid and that need for energy affects the balance between dissolved carbon dioxide and gaseous carbon dioxide at equilibrium. The harder it is for the carbon dioxide molecules to obtain the energy they need to escape from the liquid, the greater the equilibrium concentration of dissolved carbon dioxide the saturated concentration. But your wine is supersaturated, containing more than the equilibrium concentration of dissolved carbon dioxide, so carbon dioxide molecules go from liquid to gas more often than the other way around.
When the degree of supersaturation (excess gas concentration) is high, the transfer of gas molecules from liquid to gas bubble can be fast enough to make the bubbles grow in size significantly as they float up through the wine. You can see this type of rapid bubble growth in a glass of freshly poured soda, beer, or champagne. In beer, champagne, and your wine, however, the liquid surface of the bubble contains various natural chemicals that alter the interface with the gas and affect bubble growth. The "tiny bubbles" of good champagne reflect that influence.
Another way to provide the extra exposed surface in the wine and thereby allow the supersaturated dissolved gases to come out of solution would be to agitate the wine so violently that empty cavities open up within the wine. Although that approach would provide lots of extra surface, it would probably not be good for the wine. Bubbling gas through the wine is a much more gentle.
The exact choice of gas barely matters as long as it is chemically inert in the wine. Argon or helium would be just as effective, but they're more expensive (and in the case of helium, precious). The temperature of the gas doesn't matter significantly, but the temperature of the wine does. The cooler the wine, the higher the concentration of dissolved carbon dioxide and oxygen it will contain at equilibrium so you'll remove more of those gases if you do your bubbling while the wine is relatively warm.
The problem for planes isn't the temperature, it's the humidity. When the air reaches 100% relative humidity, moisture in that air begins to condense on objects such as plane wings. The moisture can also condense into rain, snow, or sleet and then fall onto those plane wings.
If the temperature of overly moist air is 32 F or below, planes preparing for takeoff can accumulate heavy burdens of ice. When water vapor condenses as ice directly onto the wings themselves, that condensation process is called deposition and is familiar to you as frost. Deposition is a relatively slow process, so most of the trouble for planes occurs when it is actually snowing or sleeting. Removing the ice then requires either heat or chemicals.
When the plane is flying at high altitudes, however, the air is extremely dry. Even though the air temperature is far below the freezing temperature of water, the fraction of water molecules in the air is nearly zero and the relative humidity is much less than 100%. That means that an ice cube suspended in that dry air would actually evaporate away to nothing. Technically, that "evaporation" of ice directly into water vapor is call sublimation and you've seen it before. Think of all the foods that have experienced freezer burn in your frost-free (i.e., extremely dry air) refrigerator or the snow that has mysteriously disappeared from the ground during a dry spell even though the temperature has never risen above freezing. Both are cases of sublimation where water molecules left the ice to become moisture in the air.
Solid ice is less dense than liquid water, meaning that a liter of ice has less mass (and weighs less) than a liter of water. Any object that is less dense than water will float at the surface of water, so ice floats.
That lower-density objects float on water is a consequence of Archimedes' principle: when an object displaces a fluid, it experiences an upward buoyant force equal in amount to the weight of the displaced fluid. If you submerge a piece of ice completely in water, that piece of ice will experience an upward buoyant force that exceeds the ice's weight because the water it displaces weighs more than the ice itself. The ice then experiences two forces: its downward weight and the upward buoyant force from the water. Since the upward force is stronger than the downward force, the ice accelerates upward. It rises to the surface of the water, bobs up and down a couple of times, and then settles at equilibrium.
At that equilibrium, the ice is displacing a mixture of water and air. Amazingly enough, that mixture weighs exactly as much as the ice itself, so the ice now experiences zero net force. That's why its at equilibrium and why it can remain stationary. It has settled at just the right height to displace its weight in water and air.
As for why ice is less dense than water, that has to do with the crystal structure of solid ice and the more complicated structure of liquid water. Ice's crystal structure is unusually spacious and it gives the ice crystals their surprisingly low density. Water's structure is more compact and dense. This arrangement, with solid water less dense than liquid water, is almost unique in nature. Most solids are denser than their liquids, so that they sink in their liquids.
Liquid water can evaporate to form gaseous water (i.e., steam) at any temperature, not just at its boiling temperature of 212 F. The difference between normal evaporation and boiling is that, below water's boiling temperature, evaporation occurs primarily at the surface of the liquid water whereas at or above water's boiling temperature, bubbles of pure steam become stable within the liquid and water can evaporate especially rapidly into those bubbles. So boiling is a just a rapid form of evaporation.
What you are actually seeing when raindrops land on warm surfaces is tiny water droplets in the air, a mist of condensation. Those droplets happen in a couple of steps. First, the surface warms a raindrop and speeds up its evaporation. Second, a small portion of warm, especially moist air rises upward from the evaporating raindrop. Third, that portion of warm moist air cools as it encounters air well above the warmed surface. The sudden drop in temperature causes the moist air to become supersaturated with moistureit now contains more water vapor than it can retain at equilibrium. The excess moisture condenses to form tiny water droplets that you see as a mist.
This effect is particularly noticeable when it's raining because the humidity in the air is already very near 100%. The extra humidity added when the warmed raindrops evaporate is able to remain gaseous only in warmed air. Once that air cools back to the ambient temperature, the moisture must condense back out of it, producing the mist.
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