Ideal Gas Law

The ideal gas model is used to predict the behavior of gases and is one of the most useful and commonly used substance models ever developed. I was found, that if we confine 1 mol samples of various gases in identical volume and hold the gases at the same temperature, then their measured pressures are almost the same. Moreover when we confine gases at lower densities the differences tend to disappear.

Any equation that relates the pressure, temperature, and specific volume of a substance is called an equation of state. The simplest and best-known equation of state for substances in the gas phase is the Ideal Gas equation of state. It was first stated by Émile Clapeyron in 1834 as a combination of the empirical Boyle’s law, Charles’ law and Avogadro’s Law. This equation predicts the p-v-T behavior of a gas quite accurately for dilute or low-pressure gases. In an ideal gas, molecules have no volume and do not interact. According to the ideal gas law, pressure varies linearly with temperature and quantity, and inversely with volume.

pV = nRT

Enthalpy - Example - A frictionless piston

where:

p is the absolute pressure of the gas

n is the amount of substance

T is the absolute temperature

V is the volume

R  is the ideal, or universal, gas constant, equal to the product of the Boltzmann constant and the Avogadro constant. The power of the ideal gas law is in its simplicity. When any two of the thermodynamic variables, p, v, and T are given, the third can easily be found.

The ideal gas model is based on following assumptions:

  1. The pressure, volume, and temperature of an ideal gas obey the ideal gas law.
  2. The specific internal energy is only a function of the temperature: u = u(T)
  3. The molar mass of an ideal gas is identical with the molar mass of the real substance
  4. The specific heats — cp and cv — are independent of temperature which means that they are constants.

From microscopic point of view it is based on these assumptions:

  1. The molecules of the gas are small, hard spheres.
  2. The only forces between the gas molecules are those that determine the point-like collisions.
  3. All collisions are elastic and all motion is frictionless.
  4. The average distance between molecules is much larger than the size of the molecules.
  5. The molecules are moving in random directions.
  6. There are no other attractive or repulsive force between these molecules.

Gas Laws

In general, the gas laws are first equations of state, that correlate densities of gases and liquids to temperatures and pressures. The gas laws were completely developed at the end of the 18th century. These laws or statements precededthe ideal gas law, since individually these laws are considered as special cases of the ideal gas equation, with one or more of the variables held constant. Since they have been almost completely replaced by the ideal gas equation, it is not usual for students to learn these laws in detail. The ideal gas equation was first stated by Émile Clapeyron in 1834 as a combination of these laws: