A submerged object's buoyancy (the upward force exerted on it by a fluid) is exactly equal to the weight of the fluid it displaces. In this case, the upward buoyant force on the bathysphere is equal in amount to the weight of the water it displaces. Since the bathysphere is essentially incompressible, it always displaces the same volume of water. And since water is essentially incompressible, that fixed volume of water always weighs the same amount. That's why the bathysphere experiences a constant upward force on it due to the surrounding water. To sink the bathysphere, they weight it down with heavy metal particles. And to allow the bathysphere to float back up, they release those particles and reduce the bathysphere's total weight.
The simple answer to your question is yes, you can do it. But you'll encounter two significant problems with trying to turn your ordinary TV into a projection system. First, the lens you'll need to do the projection will be extremely large and expensive. Second, the image you'll see will be flipped horizontally and vertically. You'll have to hang upside-down from your porch railing, which will make drinking a beer rather difficult.
About the lens: in principle, all you need is one convex lens. A giant magnifying glass will do. But it has a couple of constraints. Because your television screen is pretty large, the lens diameter must also be pretty large. If it is significantly smaller than the TV screen, it won't project enough light onto your wall. And to control the size of the image it projects on the wall, you'll need to pick just the right focal length (curvature) of the lens. You'll be projecting a real image on the wall, a pattern of light that exactly matches the pattern of light appearing on the TV screen. The size and location of that real image depends on the lens's focal length and on its distance from the TV screen. You'll have to get these right or you'll see only a blur. Unfortunately, single lenses tend to have color problems and edge distortions. Projection lenses need to be multi-element carefully designed systems. Getting a good quality, large lens with the right focal length is going to cost you.
The other big problem is more humorous. Real images are flipped horizontally and vertically relative to the light source from which they originate. Unless you turn your TV set upside-down, your wall image will be inverted. And, without a mirror, you can't solve the left-right reversal problem. All the writing will appear backward. Projection television systems flip their screen image to start with so that the projected image has the right orientation. Unless you want to rewire your TV set, that's not going to happen for you. Good luck.
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.
The spoon will have essentially no effect at all on the food. Metal left in the microwave oven during cooking will only cause trouble if (a) it is very thin or (b) it has sharp edges or points. The microwaves push electric charges back and forth in metal, so if the metal is too thin, it will heat up like the filament of a light bulb and may cause a fire. And if the metal has sharp edges or points, charges may accumulate on those sharp spots and then leap into space as a spark. But because your spoon was thick and had rounded edges, the charges that flowed through it during cooking didn't have any bad effects on the spoon: no heating and no sparks.
As far as the food is concerned, the presence of the spoon redirected the microwaves somewhat, but probably without causing any noticeable changes in how the food cooked. There is certainly no residual radiation of any sort and the food is no more likely to cause cancer after being cooked with metal around than had there been no spoon with it. In general, leaving a spoon in a cup of coffee or bowl of oatmeal isn't going to cause any trouble at all. I do it all the time. In fact, having a metal spoon in the liquid may reduce the likelihood of superheating the liquid, a dangerous phenomenon that occurs frequently in microwave cooking. Superheated liquids boil violently when you disturb them and can cause serious injuries as a result.
Water doesn't always boil when it is heated above its normal boiling temperature (100 °C or 212 °F). The only thing that is certain is that above that temperature, a steam bubble that forms inside the body of the liquid will be able to withstand the crushing effects of atmospheric pressure. If no bubbles form, then boiling will simply remain a possibility, not a reality. Something has to trigger the formation of steam bubbles, a process known as "nucleation." If there is no nucleation of steam bubbles, there will be no boiling and therefore no effective limit to how hot the water can become.
Nucleation usually occurs at hot spots during stovetop cooking or at defects in the surfaces of cooking vessels. Glass containers have few or no such defects. When you cook water in a smooth glass container, using a microwave oven, it is quite possible that there will be no nucleation on the walls of the container and the water will superheat. This situation becomes even worse if the top surface of the water is "sealed" by a thin layer of oil or fat so that evaporation can't occur, either. Superheated water is extremely dangerous and people have been severely injured by such water. All it takes is some trigger to create the first bubble-a fork or spoon opening up the inner surface of the water or striking the bottom of the container-and an explosion follows. I recently filmed such explosions in my own microwave (low-quality movie (749KB), medium-quality movie (5.5MB)), or high-quality movie (16.2MB)). As you'll hear in my flustered remarks after "Experiment 13," I was a bit shaken up by the ferocity of the explosion I had triggered, despite every expectation that it would occur. After that surprise, you'll notice that I became much more concerned about yanking my hand out of the oven before the fork reached the water. I recommend against trying this dangerous experiment, but if you must, be extremely careful and don't superheat more than a few ounces of water. You can easily get burned or worse. For a reader's story about a burn he received from superheated water in a microwave, touch here.
Here is a sequence of images from the movie of my experiment, taken 1/30th of a second apart:
I'm afraid that there's no easy answer to this question. You can use a microwave oven to superheat water in any container that doesn't assist bubble formation. How a particular container behaves is hard for me to say without experimenting. I'd heat a small amount of water (1/2 cup or less) in the container and look at it through the oven's window to see if the water boils nicely, with lots of steam bubbles streaming upward from many different points on the inner surface of the container. The more easily water boils in the container, the less likely it is to superheat when you cook it too long. (If you try this experiment, leave the potentially superheated water in the closed microwave oven to cool!)
Glass containers are clearly the most likely to superheat water because their surfaces are essentially perfect. Glasses have the characteristics of frozen liquids and a glass surface is as smooth as... well, glass. When you overheat water in a clean glass measuring cup, your chances of superheating it at least mildly are surprisingly high. The spontaneous bubbling that occurs when you add sugar, coffee powder, or a teabag to microwave-heated water is the result of such mild superheating. Fortunately, severe superheating is much less common because defects, dirt, or other impurities usually help the water boil before it becomes truly dangerous. That's why most of us avoid serious injuries.
However, even non-transparent microwaveable containers often have glass surfaces. Ceramics are "glazed," which means that they are coated with glass for both sealing and decoration. Many heavy mixing bowls are glass or glass-ceramics. As you can see, it's hard to get away from trouble. I simply don't know how plastic microwaveable containers behave when heating water; they may be safe or they may be dangerous.
If you're looking for a way out of this hazard, here are my suggestions. First, learn to know how long a given amount of liquid must be heated in your microwave in order to reach boiling and don't cook it that long. If you really need to boil water, be very careful with it after microwaving or boil it on a stovetop instead. My microwave oven has a "beverage" setting that senses how hot the water is getting. If the water isn't hot enough when that setting finishes, I add another 30 seconds and then test again. I never cook the water longer than I need to. Cooking water too long on a stovetop means that some of it boils away, but doing the same in a microwave oven may mean that it becomes dangerously superheated. Your children can still "cook" soup in the microwave if they use the right amount of time. Children don't like boiling hot soup anyway, so if you figure out how long it takes to heat their soup to eating temperature and have them cook their soup only that long, they'll never encounter superheating. As for dad's coffee water, same advice. If dad wants his coffee boiling hot, then he should probably make it himself. Boiling water is a hazard for children even without superheating.
Second, handle liquids that have been heated in a microwave oven with respect. Don't remove a liquid the instant the oven stops and then hover over it with your face exposed. If the water was bubbling spasmodically or not at all despite heavy heating, it may be superheated and deserves particular respect. But even if you see no indications of superheating, it takes no real effort to be careful. If you cooked the water long enough for it to reach boiling temperature, let it rest for a minute per cup before removing it from the microwave. Never put your face or body over the container and keep the container at a safe distance when you add things to it for the first time: powdered coffee, sugar, a teabag, or a spoon.
Finally, it would be great if some entrepreneurs came up with ways to avoid superheating altogether. The makers of glass containers don't seem to recognize the dangers of superheating in microwave ovens, despite the mounting evidence for the problem. Absent any efforts on their parts to make the containers intrinsically safer, it would be nice to have some items to help the water boil: reusable or disposable inserts that you could leave in the water as it cooked or an edible powder that you could add to the water before cooking. Chemists have used boiling chips to prevent superheating for decades and making sanitary, nontoxic boiling sticks for microwaves shouldn't be difficult. Similarly, it should be easy to find edible particles that would help the water boil. Activated carbon is one possibility.
Last night's report wasn't meant to scare you away from using your microwave oven or keep you from heating water in it. It was intended to show you that there is a potential hazard that you can avoid if you're informed about it. Microwave ovens are wonderful devices and they prepare food safely and efficiently as long as you use them properly. "Using them properly" means not heating liquids too long in smooth-walled containers.
Superheated water doesn't always wait until triggered before undergoing sudden boiling. All that's needed to start an explosion is for something to introduce an initial "seed" bubble into the liquid. Sometimes the container already has everything necessary to form a seed bubble and it's just a matter of getting the water hot enough to start that process. Many seed bubbles begin as trapped air in tiny crevices. As the water gets hotter, the size of any trapped air pocket grows and eventually it may be able to break free as a real seed bubble. When water is sufficiently superheated, just a single seed bubble is enough to start an explosion and empty the container completely. In your case, the coffee flash boiled spontaneously after something inside it nucleated the first bubble.
This sort of accident happens fairly often and we rarely think much about it as we sponge up the spilled liquid inside the microwave oven. But had your friend been unlucky enough to stop heating the coffee a second or two before that POP, she might have been injured while taking the coffee out of the oven. The moral of this story is to avoid overcooking any liquid in the microwave oven. If you must drink your coffee boiling hot, pay attention to it as it heats up so that it doesn't cook too long and then let it sit for a minute after the oven turns off. If you don't like your coffee boiling hot, then don't heat it to boiling at all.
The bulb will operate perfectly well, regardless of which way you connected the lamp's two wires. Current will still flow in through one wire, pass through the bulb's filament, and return to the power company through the other wire. The only shortcoming of reversing the connections is that you will end up with the "hot" wire connected to the outside of the socket and bulb, rather than to the central pin of the socket and bulb. That's a slight safety issue: if you touch the hot wire with one hand and a copper pipe with the other, you'll get a shock. That's because a large voltage difference generally exists between the hot wire and the earth itself.
In contrast, there should be very little voltage difference between the other wire (known as "neutral") and the earth. In a properly wired lamp, the large spade on the electric plug (the neutral wire) should connect to the outside of the bulb socket. That way, when you accidentally touch the bulb's base as you screw it in or out, you'll only be connecting your hand to the neutral wire and won't receive a shock. If you miswire the lamp and have the hot wire connected to the outside of the socket, you can get a shock if you accidentally touch the bulb base at any time.
When you put fans in front of the vents, you are probably causing the air conditioner to pump roughly the same amount of heat out of the room air as it would at 75 °F without the fans. As a result, the fans probably aren't making the air conditioner work less and aren't saving much electricity. In fact, the fans themselves consume electricity and produce heat that the air conditioner must then remove, so in principle the fans are a waste of energy.
However, if the fans are directing the cold air in a way that makes you more comfortable without having to cool all the room air or if the fans are creating fast moving air that cools you via evaporation more effectively, then you may be experiencing a real savings of electricity.
To figure out which is the case, you'd have to log the time the air conditioner cycles on during a certain period while the fans were off and the thermostat set to 75 °F and then repeat that measurement during a similar period with the fans on and the thermostat set to 78 °F. If the fans significantly reduce the units runtime while leaving you just as comfortable, then you're saving power.
The cooking chamber of a microwave oven has mesh-covered holes to permit air to enter and exit. The holes in the metal mesh are small enough that the microwaves themselves cannot pass through and are instead reflected back into the cooking chamber. However, those holes are large enough that air (or light in the case of the viewing window) can pass through easily. Sending air through the cooking chamber keeps the cooking chamber from turning into a conventional hot oven and it carries food smells out into the kitchen.