Example of Ideal and Real Gas

Compare ideal and real gases by the gas equation assumed that the gaseous molecule which obeys ideal gas law under all conditions of temperature and pressure are the example ideal gases but which does not obey are the example real one. This gas formula can use for comparison of the physical property, thermal expansion, and compression of ideal and real gases.

An ideal gas, really hypothetical one, because under the maintained temperature and pressure they transformed into a liquid state but we assumed that perfect gases molecule have no intermolecular attraction.

Compare the property of ideal gases and real gas molecule

Physical Properties of the Ideal Gases

  1. An ideal gas can not be liquefied because the gaseous molecule has no inter-molecular attraction.
  2. The coefficient of thermal expansion(ɑ) depends on the temperature of the gases and does not depends on nature.
  3. The coefficient of compressibility(β) similarly depends on the pressure and will be the same for all gases.
  4. When pressure is plotted against volume at a constant temperature a rectangular hyperbola curve is obtained.
  5. When PV is plotted against pressure at a constant temperature a straight line parallel plot obtained.
  6. If the gases molecule passes through a porous plug from higher pressure to lower pressure within the insulated enclosure, there will be no change in the temperature. This confirms that the ideal gases have no inter-molecular attraction.

Thermal Expansion and Compressibility Formula of Ideal Gas

The thermodynamic formula of the coefficient of thermal expansion  and compressibility of a gas

Compare thermal expansion and compressibility of the ideal gaseous molecule

The thermal expansion coefficient
α = R/PV = 1/T

Therefore thermal expansion will be independent of nature and will be a function of temperature only. For example, the coefficient of thermal expansion for hydrogen and carbon dioxide gases 2.78 × 10-7 and 3.49 × 10-7 respectively at 0°C and 500 atmospheres.

Compressibility factor
β = RT/P2V = 1/P

Therefore, β should be a function of pressure only and the same for all gases. But experimentally the coefficient of compressibility has been found to be individual property.

Physical Properties of Real Gases

  1. Real gas could be liquefied because the gaseous molecule has the property of intermolecular attraction which helps to coalesce the molecule.
  2. The coefficient of thermal expansion (α) depends on the nature of the gaseous molecule.
  3. The coefficient of compressibility (β) also is found to depend on the nature of the gases.
  4. When pressure plotted against volume a rectangular hyperbola curve obtained only at a high temperature above the critical temperature.
  5. But a temperature below the critical temperature (TC), the molecule can be liquefied after certain pressure depends on temperature. Liquid and gas can be indistinguishable property in the critical point of the gases.
    When PV is plotted against pressure for real or Van der Waals gases, the Amagat curve obtained.
  6. Real gases pass through porous plug from higher pressure to lower pressure within the insulated enclosure, there occurs a change of temperature.
  7. Real gases have inter-molecular attraction and when expands, the molecules have to spend more kinetic energy to overcome inter-molecular attraction compare to an ideal gas. Therefore, the temperature drops down.

Example of compression of the Gas

The value of Z decreases attains minimum and then increases with the increased pressure. Hydrogen and helium gas have baffled this compression trend and the curve rise with increased pressure from the very beginning. Carbon dioxide can be easily liquified and Z dips sharply below the ideal gas line in the low-pressure region.

TB called Boyle temperature, the initial slope at TB zero. At TB, the Z vs P line of the tangent to that of real gas when pressure approaches zero but latter rises above the ideal line only very slowly. Thus, at TB real gas behaves ideally over a wide range of pressure, because the effect of the size of the gaseous molecule and intermolecular forces roughly compensate each other.

Gaseous Molecule Boyle Temp (TB)
Hydrogen (H2) -1560C
Helium (He) -2490C
Nitrogen (N2) 590C
Methane (CH4) 2240C
Ammonia (NH3) 5870C

For hydrogen and helium, TB lowers then 0⁰C temperature so Z values greater than unity. For nitrogen, methane, and ammonia gas TB greater compare then 0⁰C, thus Z values less than unity in the low-pressure region.

Compressibility for Real Gas

An example of a single parameter called the compressibility used to compare the extent of deviation of the real gases from ideal behavior.


  1. When Z=1, there is no deviation from the ideal behavior.
  2. When Z ≠ 1, the departure of the value of Z from unity is a measure of the extent of non-ideality.
  3. Zく1, the gas is a more compressible then ideal gases, and when Z 〉1, less compressible then ideal gases.