The Kinetic Theory of Gases and Liquefaction

The kinetic theory of gases is a model that explains the behavior of gases based on the motion and interaction of their individual particles. According to this theory, a gas is composed of a large number of small particles (atoms or molecules) that are in constant random motion.

Liquefaction of Gases

Liquefaction of a gas refers to the process of converting a gas into its liquid state. This can be achieved by reducing the temperature and/or increasing the pressure of the gas. When a gas is cooled or compressed, the average kinetic energy of its particles decreases, and the intermolecular forces become strong enough to hold the particles closer together, resulting in the formation of a liquid.

The Critical Point

The critical point of a substance is the temperature and pressure at which its gas and liquid states become indistinguishable. At this point, the substance exhibits unique properties that cannot be attributed to either the gas or liquid phase. The critical temperature (TC) is the highest temperature at which the substance can exist as a liquid, and the critical pressure (PC) is the minimum pressure required to liquefy the substance at its critical temperature.

Explanation of the Correct Answer

The correct answer to the given question is option 'D' - It cannot be liquefied at any value of P and T. This means that there are certain gases that cannot be liquefied under any conditions, regardless of the pressure or temperature applied.

These gases are known as "permanent gases" or "ideal gases" and include substances such as helium and neon. According to the kinetic theory of gases, ideal gases have particles that are in constant motion and do not interact with each other. As a result, they do not possess intermolecular forces that are strong enough to cause liquefaction.

Since these gases lack attractive forces between their particles, no amount of pressure or cooling can cause them to condense into a liquid state. Therefore, they cannot be liquefied under any conditions.

It is important to note that the other options mentioned in the question (a, b, and c) are incorrect. For liquefaction to occur, the pressure must be greater than the critical pressure (PC) at a temperature less than the critical temperature (TC). These conditions are necessary but not sufficient for liquefaction. The substance must also have intermolecular forces that can be overcome by the applied pressure or cooling. In the case of ideal gases, these forces are absent, leading to their inability to be liquefied.

In conclusion, according to the kinetic theory of gases, ideal gases cannot be liquefied under any conditions due to the absence of intermolecular forces. These gases remain in the gaseous state regardless of the pressure or temperature applied, making option 'D' the correct answer.