Almost the instant the nuclear fuel reaches critical mass, it begins to release heat and explode. If this fuel overheats and rips itself apart before most its nuclei have undergone fission, only a small fraction of the fuel's nuclear energy will have been released in the explosion. There are at least two possible causes for such a "fizzle": slow assembly of the super-critical mass needed for explosive chain reactions and poor containment of the exploding fuel. A well designed fission bomb assembles its super-critical mass astonishingly quickly and it shrouds that mass in an envelope that prevents it from exploding until most of the nuclei have had time to shatter.
Critical, sub-critical, and super-critical mass all refer to the chain reactions that occur in fissionable material—a material in which nuclei can shatter or "fission" when struck by a passing neutron. When this nuclear fuel is at critical mass, each nucleus that fissions directly induces an average of one subsequent fission. This situation leads to a steady chain reaction in the fuel: the first fission causes a second fission, which causes a third fission, and so on. Steady chain reactions of this sort are used in nuclear reactors.
When the fuel is below critical mass, there aren't quite enough nuclei around to keep the chain reactions proceeding steadily and each chain gradually dies away. While such a sub-critical mass of fuel continues to experience chain reactions, they aren't self-sustaining and depend on natural radioactive decay to restart them.
When the fuel is above critical mass, there are more than enough nuclei around to sustain the chain reactions. In fact, each chain reaction grows exponentially in size with the passage of time. Since each fission directly induces more than one subsequent fission, it takes only a few generations of fissions before there are astronomical numbers of nuclei fissioning in the fuel. Explosive chain reactions of this sort occur in nuclear weapons.
A nuclear reactor operates just below critical mass so that each radioactive decay in its fuel rods induces a large but finite number of subsequent fissions. Since each chain reaction gradually weakens away to nothing, there is no danger that the fuel will explode. But operating just below critical mass is a tricky business and it involves careful control of the environment around the nuclear fuel rods. The operators use neutron absorbing control rods to dampen the chain reactions and keep the fuel just below critical mass.
Fortunately, there are several effects that make controlled operation of a reactor relatively easy. Most importantly, some of the neutrons involved in the chain reactions are delayed because they come from radioactive decay processes. These delayed neutrons slow the reactor's response to changes—the chain reactions take time to grow stronger and they take time to grow weaker. As a result, it's possible for a reactor to exceed critical mass briefly without experiencing the exponentially growing chain reactions that we associate with nuclear explosions. In fact, the only nuclear reactor that ever experienced these exponentially growing chain reactions was Chernobyl. That flawed and mishandled reactor went so far into the super-critical regime that even the neutron delaying effects couldn't prevent exponential chain reactions from occurring. The reactor superheated and ripped itself apart.
While the cannonball is in your boat, its great weight pushes the boat deeper into the water. To support the cannonball, the boat must displace the cannonball's weight in water—a result known as Archimedes principle. Since the cannonball is very dense, the boat must displace perhaps 8 cannonball volumes of water in order to obtain the buoyancy needed to support the cannonball. This displaced water appears on the surface of the lake so that the lake's level rises.
Now suppose that you throw the cannonball overboard. The cannonball quickly sinks to the bottom. The boat now floats higher than before because it no longer needs to displaces the extra 8 cannonball volumes of water. Although the cannonball itself is displacing 1 cannonball volume of water, there are still 7 cannonball volumes less water being displaced by objects in the water. As a result, the water level of the lake drops slightly when you throw the cannonball overboard.
You're right. The greater the temperature difference between two objects, the faster heat flows between them. This effect is useful whenever you forget to chill drinks for a party. Just don't leave a glass bottle in the freezer too long; if the water inside freezes, it may expand enough to break the bottle.
A hot water heater is built so that hot water is drawn out of its top and cold water enters it at its bottom. Since hot water is less dense than cold water, the hot water floats on the cold water and they don't mix significantly. As you take your shower, you slowly deplete the hot water at the top of the tank and the level of cold water rises upward. But the shower doesn't turn cold until almost all the hot water has left the tank and the cold water level has risen to its top.
When you simply heat the cold air, you lower its relative humidity—the heated air is holding a smaller fraction of its maximum water molecule capacity and is effectively dry. Dry air always feels colder than humid air at the same temperature. That's because water molecules are always evaporating from your skin. If the air is dry, these evaporating molecules aren't replaced and they carry away significant amounts of heat. On a hot day, this evaporation provides pleasant cooling but on a cold day it's much less welcome. If the air near your skin is humid, water molecules will return to your skin almost as frequently as they leave and will bring back most of the heat that you would have lost to evaporation. Thus humid air spoils evaporative cooling, making humid weather unpleasant in the summer but quite nice in the winter.
The simple answer is entropy—the ever-increasing disorder of the universe. Salt water is far more disordered than the salt and water from which it's formed, so separating those components doesn't happen easily. The second law of thermodynamics observes that the entropy of an isolated system cannot decrease—you can't reduce the disorder of the salty water without paying for it elsewhere. In effect, you have to export the salty water's disorder somewhere else as you separate it into pure water and pure salt.
In most cases, this exported disorder winds up in the energy used to desalinating sea water. You start with nicely ordered energy—perhaps electricity or gasoline—and you end up with junk energy such as waste heat. While some desalination techniques such as reverse osmosis can operate near the efficiency limits imposed by thermodynamics, they can't avoid those limits. If you want to desalinate water, you must consume ordered resources and those resources usually cost money (an exception is sunlight). The desalinating equipment is also expensive. Until water becomes scarce enough or energy cheap enough, desalinated water will remain uncommon in the United States.
Not without using something other than pure, normal water for the ice. The density of ice is always less than that of water at the same pressure. While squeezing the ice will increase its density, it will also increase the density of the water so the ice will always float. Of course, you could add dense materials to the ice to weight it down to neutral buoyancy, but then it wouldn't be pure ice any more.
The microwave oven is superheating the water to a temperature slightly above its boiling temperature. It can do this because it doesn't help water boil the way a normal coffee maker does. For water to boil, two things must occur. First, the water must reach or exceed its boiling temperature—the temperature at which a bubble of pure steam inside the water becomes sturdy enough to avoid being crushed by atmospheric pressure. Second, bubbles of pure steam must begin to nucleate inside the water. It's the latter requirement that's not being met in the water you're heating with the microwave. Steam bubbles rarely form of their own accord unless the water is far above its boiling temperature. That's because a pure nucleation event requires several water molecules to break free of their neighbors simultaneously to form a tiny steam bubble and that's very unlikely at water's boiling temperature. Instead, most steam bubbles form either at hot spots, or at impurities or imperfections—scratches in a metal pot, the edge of a sugar crystal, a piece of floating debris. When you heat clean water in a glass container using a microwave oven, there are no hot spots and almost no impurities or imperfections that would assist boiling. As a result, the water has trouble boiling. But as soon as you add a powder to the superheated water, you trigger the formation of steam bubbles and the liquid boils madly.