•••Eliza Snow/iStock/Getty Images
Before we can calculate the density of carriers in a semiconductor, we have to find the number of available states at each energy. The number of electrons at.
By W.D. Johnson
Gases were an enigma to early scientists who were baffled by their freedom of movement and apparent weightlessness compared to liquids and solids. In fact, they did not determine that gases constituted a state of matter until the 17th century. Upon closer study, they began observing consistent properties that defined gases. The single distinction that initially baffled scientists -- that of gas particles having more space to move freely than particles of solids or liquids -- informs each of the properties that all gases have in common.
Low Density
Gases contain scattered molecules that are dispersed across a given volume and are therefore less dense than in their solid or liquid states. Their low density gives gases fluidity, which allows gas particles to move rapidly and randomly past one another, expanding or contracting with no fixed positioning. The average distances between the molecules are large enough that interactions between molecules don't interfere with their motion.
Indefinite Shape or Volume
Gases have no definite shape or volume.The random movement of gas molecules allows them to expand or contract to assume the volume of the container holding them. Therefore, a gas's volume refers to the space of the container in which its molecules have range to move. This property results in gases occupying more space than they would in their liquid or solid state. Gases also contract and expand by predictable amounts depending upon changes in temperature and pressure.
Compressibility and Expandability
The low density of gases makes them compressible since their molecules can be positioned far apart from one another. This allows them to move freely to fit into the gaps of space between them. Just as gases are compressible, they are also expandable. The freedom of gas molecules causes them to take the shape of any container in which they are placed, filling the container's volume.
Diffusivity
Given the large amounts of space between gas molecules, two or more gases can mix quickly and easily with one another to form a homogeneous mixture. This process is called diffusion.
Pressure
Gas molecules are in constant motion. They exert pressure, or force per unit area, on the interior surface of their container. The pressure varies according to the amount of gas confined to a given container's volume, the temperature and the pressure.
- Eliza Snow/iStock/Getty Images
Gas is a state of matter that has no fixed shape and no fixed volume. Gases have lower density than other states of matter, such as solids and liquids. There is a great deal of empty space between particles, which have a lot of kinetic energy. The particles move very fast and collide into one another, causing them to diffuse, or spread out, until they are evenly distributed throughout the volume of the container.
When more gas particles enter a container, there is less space for the particles to spread out, and they become compressed. The particles exert more force on the interior volume of the container. This force is called pressure. There are several units used to express pressure. Some of the most common are atmospheres (atm), pounds per square inch (psi), millimeters of mercury (mmHg) and pascals (Pa). The units relate to one another this way: 1 atm = 14.7 psi = 760 mmHg = 101.3 kPa (1,000 pascals).
Besides pressure, denoted in equations as P, gases have other measurable properties: temperature (T), volume (V) and number of particles, which is expressed in a mole number (n or mol). In work involving gas temperature, the Kelvin scale is often used.
Because temperature and pressure vary from place to place, scientists use a standard reference point, called standard temperature and pressure (STP), in calculations and equations. Standard temperature is the freezing point of water — 32 degrees Fahrenheit (0 degrees Celsius, or 273.15 Kelvin). Standard pressure is one atmosphere (atm) — the pressure exerted by the atmosphere on Earth at sea level.
Gas laws
Temperature, pressure, amount and volume of a gas are interdependent, and many scientists have developed laws to describe the relationships among them.
Boyle's law
Boyle's law is named after Robert Boyle, who first stated it in 1662. Boyle's law states that if temperature is held constant, volume and pressure have an inverse relationship; that is, as volume increases, pressure decreases, according to the University of California, Davis' ChemWiki. Increasing the amount of space available will allow the gas particles to spread farther apart, but this reduces the number of particles available to collide with the container, so pressure decreases. Decreasing the volume of the container forces the particles to collide more often, so pressure is increased. A good example of this is when you fill a tire with air. As more air goes in, the gas molecules get packed together, reducing their volume. As long as the temperature stays the same, the pressure increases.
Charles' law (Gay-Lussac's law)
In 1802, Joseph Louis Gay-Lussac, a French chemist and physicist referenced data gathered by his countryman, Jacque Charles, in a paper describing the direct relationship between the temperature and volume of a gas kept at a constant pressure. Most texts refer to this as Charles' law, but a few call it Gay-Lussac's law, or even the Charles Gay-Lussac law.
This law states that the volume and temperature of a gas have a direct relationship: As temperature increases, volume increases, when pressure is held constant. Heating a gas increases the kinetic energy of the particles, causing the gas to expand. In order to keep the pressure constant, the volume of the container must be increased when a gas is heated.
This law explains why it is an important safety rule that you should never heat a closed container. Increasing temperature without increasing the volume available to accommodate the expanding gas means that pressure builds up inside the container and may cause it to explode. The law also explains why a turkey thermometer pops out when the turkey is done: The volume of air trapped under the plunger increases as the temperature inside the turkey climbs.
Avogadro's number
In 1811, Italian scientist Amedeo Avogadro proposed the idea that equal volumes of gas at the same temperature and pressure will have an equal number of particles, regardless of their chemical nature and physical properties.
Ideal gas constant
The kinetic energy per unit of temperature of one mole of a gas is a constant value, sometimes referred to as the Regnault constant, named after the French chemist Henri Victor Regnault. It is abbreviated by the letter R. Regnault studied the thermal properties of matter and discovered that Boyle's law was not perfect. When the temperature of a substance nears its boiling point, the expansion of the gas particles is not exactly uniform.
Ideal gas law
Avogadro's Number, the ideal gas constant, and both Boyle's and Charles' laws combine to describe a theoretical ideal gas in which all particle collisions are absolutely equal. The laws come very close to describing the behavior of most gases, but there are very tiny mathematical deviations due to differences in actual particle size and tiny intermolecular forces in real gases. Nevertheless, these important laws are often combined into one equation known as the ideal gas law. Using this law, you can find the value of any of the other variables — pressure, volume, number or temperature — if you know the value of the other three.
Additional reading