Why water inside a vessel placed in a body of boiling water does not boil? Imagine a plastic sac filled with water placed in a pan of boiling water. I wonder why the water inside the sac does not boil. The temperature of the water inside the sac should be the same as that of outside water, i.e., 100 deg. celsius.
Similarly if to place a glass tumbler of water inside a pan placed on fire, the water will boil only inside the pan, but not in the tumbler.
 A: Both bodies of water will heat till 100 C (as well as the vessel). Then, the outside one will start boiling by taking latent heat from the surroundings, Now, we only have heat transfer due to conduction/radiation when there is a temperature difference (or an emf, but that's irrelevant). It's mainly conduction we need to consider, anyways. Convection won't get heat across a solid. Now, there is no temperature difference across the vessel, thus no net heat transfer. If we placed cooler water inside, there would be enough heat transfer to bring it to 100 C, and then it would stop (we can't boil pure water below 100 C at 1 atm)
So the sequence of events is as follows:


*

*Outside water starts heating

*Inside water and vessel start heating; with a small time lag

*Everything reaches 100 C (with a small time lag)

*Outside water starts boiling

*Outside water is completely boiled

*Outside water(now steam) heats up an infinitesimal amount

*Outside water continues to heat up, but also transfers heat to inner vessel. The vessel heats up and the inner water starts boiling.

*Inner water finishes boiling. Outside steam will have reached a much higher temperature (can't be calculated without knowing the masses)


Of course, since it's steam, it will probably diffuse out, so eventually only a tiny bit of the inside water will boil.
In fact, this is one of the ways one can keep a fixed mass of water at exactly 100 degrees celsius. Useful for making extremely accurate calorimetric calculations.
A: Water boils at 100° C and atmospheric pressure. If you try to boil water in a closed container, a small amount of steam will form; this will increase the pressure, and the rest of the water will not boil (unless the container bursts or leaks). This explains why water will not boil inside a plastic sac.
I don't completely understand the set-up with the tumbler, and so I can't be sure of my answer to that part. Is the tumbler sitting on the bottom of the pan surrounded by boiling water? I think the answer is that it could still boil, but at a slower rate. The glass insulates the water inside, since it's not as good a conductor of heat as the metal pan, and keeps it from being heated as fast. If the glass is a good enough insulator, the heat loss from evaporation and diffusion will keep the water inside the tumbler from boiling at all. 
A: Even if the water in the inner container reaches exactly $212 \space^\circ\mathrm F$ it still would not boil. You need to add further heat to make $212 \space^\circ \mathrm F$ water turn into $212 \space^\circ \mathrm F$ steam! This amount of heat is called latent heat because the process does not involve a temperature difference, only a change of phase. And the only way to add further heat is a temperature difference which is not possible here because the water in the bigger vessel cannot get beyond $212 \space^\circ\mathrm F$.
Water in a liquid state at $212 \space^\circ\mathrm F$ does not boil. The "boiling" we see is $212 \space^\circ\mathrm F$ steam escaping from the $212 \space^\circ \mathrm F$ water.
A: I think the answers above are missing the obvious. The bottom of a pan is generally above 100C so you get vigorous steam formation and hence the obvious boiling. The glass floating in the water is at 100C so you don't get the vigorous steam formation.
See the Wikipedia article on boiling, http://en.wikipedia.org/wiki/Boiling, and in particular on nucleate boiling. You need a temperature above the boiling point to nucleate bubbles of steam. This can happen at the bottom of the pan because it's heated by the hot gas or electric hob. The glass floating in the water cannot be heated above the boiling point.
A: To boil, water needs not only reach the boiling point, but also continually absorb heat (latent heat). The water in the sac won't boil because it can't get anymore heat from its surroundings due to being in the same temperature.
