Question

A gas can never be liquefied at (a) \(T=T_{C}\) and \(P=P_{c}\) (b) \(TT_{C}\) and \(P \gg P_{\mathrm{c}}\)

Short answer

A gas can never be liquefied at (d) T>T_{C} and P \text{ is much greater than } P_{C}.

Step-by-step solution

Understanding the Critical Point

The critical point of a substance is defined by both a critical temperature (\(T_{C}\)) and critical pressure (\(P_{C}\)). At this point, the distinction between the liquid and gas phases disappears. Above the critical temperature, no amount of pressure can liquefy the gas.

Analyzing Option (a) - At the Critical Point

If a gas is at the critical temperature (\(T=T_{C}\)) and critical pressure (\(P=P_{C}\)), it is exactly at the critical point. While the phases are indistinguishable at this point, the gas is not technically 'liquefied'.

Analyzing Option (b) - Below Critical Temperature at Critical Pressure

If the temperature is below the critical temperature (\(T<T_{C}\)) and the pressure is equal to the critical pressure (\(P=P_{C}\)), the gas can be liquefied because the temperature is within the range where liquid can exist.

Analyzing Option (c) - Below Critical Temperature and Pressure

If both the temperature is below the critical temperature (\(T<T_{C}\)) and the pressure is below the critical pressure (\(P<P_{C}\)), the gas can still potentially be liquefied by increasing the pressure.

Analyzing Option (d) - Above Critical Temperature

If the temperature is above the critical temperature (\(T>T_{C}\)), no amount of pressure applied, even if it is much greater than the critical pressure (\(P\text{ is much greater than } P_{C}\)), can liquefy the gas. This follows from the definition of the critical temperature.

Key concepts

Liquefaction of Gases

The process of turning a gas into a liquid is called liquefaction. It is a transformation that requires specific conditions to be met, typically involving temperature and pressure. When a gas is cooled or compressed, its particles slow down and come closer together, making a transition to a liquid state possible.

Understanding when and how gases liquefy is fundamental in various industries, such as in the production of liquefied natural gas (LNG) for storage and transportation. The key to liquefying a gas is managing both temperature and pressure to achieve a state where the gas molecules are compact enough to enter the liquid phase. Notably, when a substance’s temperature is below its critical temperature, it can exist as a liquid at the appropriate pressure. However, if either the critical pressure or temperature is exceeded, the gas cannot liquefy. This is because the gas molecules have too much energy or are too far apart to form liquid bonds.

Critical Temperature

The critical temperature (\(T_C\)) of a substance is the highest temperature at which that substance can exist as a liquid, regardless of the pressure applied. Once the substance reaches a temperature above its critical temperature, it transitions to a supercritical fluid state, where it exhibits properties of both gas and liquid but is neither.

For example, in refrigeration, understanding the critical temperature is essential to designing processes that cool substances below this temperature to achieve liquefaction effectively. It is also pertinent in everyday products such as the carbonation of beverages, where carbon dioxide is kept under pressure below its critical temperature to remain in a liquid state within the container. The concept of critical temperature plays a significant role in determining the conditions under which processes like the liquefaction of gases for storage and transportation can occur.

Critical Pressure

Critical pressure (\(P_C\)) is defined as the pressure required to liquefy a gas at its critical temperature. At this juncture, the liquid and gas phases of a substance exhibit the same density, and the phase boundary that separates the two disappears. Above the critical pressure, the substance is in a supercritical fluid state, where it is not possible to distinguish between the liquid and gas phases.

In industries like petrochemical and aerospace, controlling the pressure to manage the state of a gas is an integral part of operations. High-pressure technology is used to achieve and maintain supercritical states for extractions and reactions in chemical processes. Understanding critical pressure is also essential in the context of safety, as containers and systems must be designed to withstand pressures above the critical threshold to prevent accidents.