Liquid Mercury has a density of 13.55 g/cm3 at room temperature (20.0 ° C). You are trying to design a container to hold a 3.40 X 104 mg sample of mercury.
This mercury expands at 1.11 μl (microliter) per degree it is heated.
What is the minimum volume ( in liters) of the container if you want the sample to be able to be heated to 200.0 ° C? (Assume that the sample starts at room temperature.)
If this was in a sealed tube with a diameter of 0.550 cm, how tall(in cm) would the tube need to be to hold the mercury through these temperature changes? [ V= π r2h (cylinder) ] Please show your work!

A long glass tube with one end open and the other end sealed was completely filled with mercury, then it was stood on end with the open end in a container filled with mercury.

If the tube is relatively short, it will still be filled with mercury all the way to the top.  If it's long enough, the column of mercury will not reach the top.  The air pressure on the surface of the mercury pool that the tube sits in is what supports the mercury. When the weight of a 1 cm^2 column of mercury is greater than the air pressure per cm^2, it can't be supported by that pressure.  The top of the tube will have an almost perfect vacuum, with only a tiny amount of mercury vapor in it.

 The height of a column of water or mercury that can be supported by air pressure depends on, and is proportional to, the density of the water or mercury.

How you're supposed to get the answers depends on what units are used to define 1 bar of pressure. Your textbook or lecture notes should give you the value and units of a bar. If you're supposed to look it up, you'll find a variety of different combinations, including 750.06 mm of Hg or 1019.72cm of H 2 O. That would actually give you the answers directly.    

750.06 m m ≈ 0.75 m of H g

1019.72 c m ≈ 10.20 m of water

If you're supposed to calculate everything, you'll need to use 1 bar = 1 x 105 N / m 2. Then you'll have to look up the g r a v i t a t i o n constant and calculate the weight of a column of mercury or water. Note that g rams and k i l o g r a m s are units of mass, not weight, which is a force.  The unit of force in the m e t r i c system is the N e w t o n. This is confusing because we measure weight in pounds, which is a force. Most of the rest of the world measures "weight" in k i l o g r a m s, which is really mass.

How is 1 bar defined for you?

If it's m m H g, just multiply that by 13.6 to get the height for a column of water.

If it's a force per unit area:

We can calculate the force (weight) of H. g using the g r a v i t a t i o n constant and the given density, then go from there."

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