The temperature at which a real gas obeys ideal gas law over an appreciable range of pressure is called Boyle Temperature or Boyle Point.For an Ideal gas:P V = n RT LET Z = P Vreat/n R TFor an ideal gas, Z = 1 at any temperature or pressure. Boyle point depends on the nature of the real gas. Above the Boyle point Z is greater than 1.At low pressures and high temperatures much above the critical point of the substance, the real gases can be taken to behave like ideal gases. Gases like O₂, N₂,H₂, He, mono-atomic gases and inert gases behave NEARLY ideal at standard temperature (0degree C) and pressure (1 standard atmosphere).Ideal gas law does not take into account the molecular size, and inter-molecular attraction or repulsion forces. It assumes that those factors are zero. In mono-atomic gases this assumption is valid over a wide range of pressures and temperatures. But in other real gases, inter-molecular forces are weak at high temperatures and low pressures. The reason is high kinetic energy overcomes small inter-molecular forces as the molecules are separated by large distances. The molecules occupy very little space compared to the total volume of the gas.Boyle point or temperature Tb = a/Rb where a and b are Vander Waal's parameters that appear in Vander Waals gas equation and R is the universal gas constant.

Boyle Temperature

The temperature at which a real gas obeys the ideal gas laws over a wide range of pressure is known as the Boyle temperature. This temperature is specific to each gas and represents the temperature at which the compressibility factor (Z) is equal to 1.

Ideal Gas Laws

The ideal gas laws describe the behavior of an ideal or perfect gas under various conditions. These laws include Boyle's law, Charles's law, Avogadro's law, and the ideal gas equation. However, real gases deviate from ideal gas behavior at high pressures and low temperatures.

Real Gas Behavior

Unlike ideal gases, real gases interact with each other and occupy a finite volume. These interactions become significant at high pressures and low temperatures. At these conditions, the ideal gas laws fail to accurately describe the behavior of the gas.

Compressibility Factor

The compressibility factor (Z) is a dimensionless quantity that accounts for the deviations of real gases from ideal gas behavior. It is defined as the ratio of the actual volume of the gas to the volume predicted by the ideal gas law at a given temperature and pressure.

Boyle Temperature and Compressibility Factor

At the Boyle temperature, the compressibility factor of a real gas is equal to 1. This means that the gas behaves ideally over a wide range of pressure. The Boyle temperature is a characteristic property of a gas and is different for each gas.

Importance of Boyle Temperature

The Boyle temperature is significant because it represents the temperature at which a real gas can be approximated as an ideal gas over a wide range of pressure. This temperature allows for the use of simplified ideal gas equations to describe the behavior of the gas, making calculations and predictions easier.

Deviation from Ideal Gas Behavior

At temperatures below the Boyle temperature, the compressibility factor deviates from 1 as pressure increases. This indicates that the gas is no longer behaving ideally and its behavior is influenced by intermolecular forces and molecular volume.

Other Gas Temperature Points

- Critical temperature: The temperature above which a gas cannot be liquefied, regardless of pressure.
- Inversion temperature: The temperature at which a gas changes its behavior from following the ideal gas laws to deviating from them.
- Reduced temperature: The temperature of a gas expressed as a fraction of its critical temperature.

While these temperature points are also important in understanding the behavior of real gases, the specific temperature at which a real gas obeys the ideal gas laws over a wide range of pressure is the Boyle temperature.