Helium gas is stored at 100 degree C under a pressure of 5 Times 10^5 Pa in cyli
ID: 1845044 • Letter: H
Question
Helium gas is stored at 100 degree C under a pressure of 5 Times 10^5 Pa in cylindrical glass vessel 15 cm in diameter and 40 cm long. The glass walls are 1 mm thick. Over time the Helium will gradually diffuse out of the cylinder. The diffusion coefficient of He through oxide glass at 100 degree C is about 7.0 Times 10^-4 m^2/s and the concentration of He on the inner surface is about 2.2 Times 10^-3 kmol/m^3. Sketch the concentration profile of helium gas through the thickness of the cylinder walls. What is the initial rate of mass loss through the cylinder (in units of g/sec)?Explanation / Answer
When we talk about gas we usually mean the gas which is piped into our houses and which we use for heating and cooking. This is mainly a gas called methane. Methane has no smell so we usually add a harmless smelly substance to it so that we know if we have left a gas tap on or there is a gas leak. Methane comes from gas fields deep under the Earth's surface so it is often called natural gas. Natural gas, and also coal gas which was piped into our homes before the discovery of the natural gas fields under the North Sea.
There are however lots of other gases, such as oxygen, nitrogen, hydrogen, helium, chlorine, butane, propane and carbon dioxide, and of course air itself is a mixture of many different gases. Many of these gases are used in our factories, hospitals, schools and homes but they are not usually piped into them as natural gas is, they must be transported and stored in other ways. The problem is that at ordinary atmospheric temperature and pressure all gases have very low densities (a kilogram of hydrogen would fill a space 3 m by 2 m by 2 m) and it would be quite impractical to transport and store them as gases like this. We need to reduce their volume by increasing their density, and this can be done by turning them into liquids, or compressing them, or both.
Storage as a compressed liquid
The boiling point of many gases depends upon the pressure: the higher the pressure the higher the boiling point. For example the boiling point of water is 100oC at the standard atmospheric pressure of 1013 mb, but inside a pressure cooker the pressure is about 2 bars and the boiling point of water is about 120oC, while on the top of Mount Everest the pressure is only about 260 mb and the boiling point of water is about 69oC.
Similarly the boiling point of butane is about 0.5oC at atmospheric pressure, but at 2 bars it is about 20oC. So if we compress it to 2 bars it will be a liquid at all temperatures below 20oC.
Butane and many gases with boiling points of less than room temperature can be stored as liquids at room temperature by compressing them enough to raise their boiling point to the temperature of the room. Inside the container the gas is at its boiling point. The pressure inside is the pressure needed to make the boiling point of the liquid equal to the temperature of the room. If the temperature of the room then goes up slightly some of the liquid in the container turns into a gas and this raises the pressure and so also the boiling point, similarly if the temperature goes down some of the gas turns into a liquid and lowers the pressure and so also the boiling point. The pressure in the container is therefore not constant but is always the pressure needed to make the boiling point of the gas the same as the temperature of the room. As the pressure of the gas in the cylinder depends only upon the temperature of the room and not on the amount of liquid in the cylinder only a simple pressure regulator is needed.
Gases which can be stored as liquids under pressure in this way are propane and butane (sold under trade names such as Calor Gas andCamping Gaz), sulphur dioxide and ammonia and many others. (The very special case of carbon dioxide is discussed later.)
Usually these gases are stored in refillable cylinders with valves - the cylinders are very heavy and often cost more than the gas in them. At atmospheric pressure propane has a much lower boiling point than butane (see below in this Section), so at 20oC the pressure inside a propane cylinder is about 5 bars, but that inside a butane cylinder is only about 2 bars. So small quantities of butane for recreational use (Camping Gaz etc) are often sold in light-weight disposable cartridges. For the safe handling of these cartridges see the section on Safety at the end of this page. We can also store some other gases, such as sulphur dioxide, in light-weight disposable cartridges, but not propane as the pressure is much higher so the container needs to be much stronger and would not be light-weight!
Cylinders containing inflammable gases are usually fitted with connectors with left-hand threads, where to tighten the nut you have to turn it anti-clockwise. This is intended to make it impossible to connect a cylinder containing an inflammable gas to a pipe intended to carry oxygen or air or any non-inflammable gas.
A butane cylinder contains both liquid and gas. When we open the valve we want only gas to come out: we must therefore always use the cylinder in an upright position, and also always let it stand for a few minutes after moving it, to allow the liquid to settle, before using it. If any liquid were to pass through the valve with the gas, when it reached the burner it would flare up in a highly dangerous way.
The boiling point of butane at atmospheric pressure is minus 0.5oC, which means that when the temperature is below freezing point the pressure in a butane cylinder is atmospheric and when you turn on the tap nothing will come out. Even at slightly higher temperatures the pressure is very low so butane cannot be used out of doors in the winter. For this reason most building and other industrial sites, and also hot-air balloonists, use propane not butane - the boiling point of propane at atmospheric pressure is minus 42oC, and even at -25oC the pressure in the cylinder is more than 2 bars.
LPG (Liquefied petroleum gas) is the generic name for commercial butane and propane.
Storage as a compressed gas
Oxygen, nitrogen and many other gases have what is called a critical temperature. Above its critical temperature a gas cannot be liquefied by pressure alone. The critical temperature for butane is 152oC so below this temperature it can be liquefied just by compressing it. But the critical temperature for oxygen is minus 118oC, which means that above this temperature we cannot liquify it just by compressing it, no matter how much hard we try. All the gases in the air (except carbon dioxide which is discussed later), and also hydrogen, methane and ethane and many other gases have critical temperatures below room temperature.
We can store these gases in cylinders at high pressure, sometimes up to several hundred times atmospheric pressure - the higher the pressure the greater the amount we can store in the cylinder. As we use up the gas the pressure in the cylinder falls so we need a very complex pressure regulator to maintain a constant rate of flow out of the cylinder. The cylinders must be very strong and so are very heavy and expensive: they cost a lot more than the gas inside them!
Some gases that are often stored in this way are
The special case of carbon dioxide is discussed later.
Hybrid solutions are not feasible. For example the critical temperature for ozone is about -12oC so you could store ozone as a liquid under pressure in a freezer. The problem is, what happens if there is a power cut and the freezer goes off?
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