The correct answer is option 'C', which is the critical temperature. Let's understand the concept in detail.

Gas and Liquefaction

Gases are one of the three states of matter, along with solids and liquids. Gases do not have a definite shape or volume, and they tend to expand to fill their container completely. They also have a low density and are highly compressible.

Liquefaction is the process of converting a gas into a liquid. This process is achieved by reducing the temperature and increasing the pressure of the gas. When the pressure and temperature of a gas are increased, its particles come closer to each other, and the gas starts to condense into its liquid form.

Critical Temperature

The critical temperature is the highest temperature at which a gas can be liquefied, regardless of the pressure applied. Above this temperature, no amount of pressure can cause the gas to liquefy. At the critical temperature, the gas has a unique property where the distinction between the liquid and gas phases disappears. The gas is said to be in a supercritical state.

The critical temperature is different for each gas and depends on the intermolecular forces between its particles. For example, the critical temperature of water is 374°C, while the critical temperature of carbon dioxide is 31°C.

Boyle Temperature and Inversion Temperature

Boyle temperature is the temperature at which a gas cannot be liquefied, even at very high pressures. It is named after Robert Boyle, who first described the relationship between the pressure and volume of gases.

Inversion temperature is the temperature at which the Joule-Thomson coefficient of a gas changes sign from positive to negative. This temperature is different for each gas and depends on its intermolecular forces.

Conclusion

In summary, a gas cannot be liquefied above its critical temperature, regardless of the pressure applied. The critical temperature is a unique property of each gas and depends on the intermolecular forces between its particles. The Boyle temperature and inversion temperature are different concepts and do not determine the liquefaction of a gas.

At a temperature equal to the critical temperature, the density and all other properties of the liquid and vapor become equal. Hence, it is impossible to liquefy a gas above this temperature irrespective of how high the pressure might be.