Question

A gas can be liquefied by pressure alone when its temperature is (1) higher than its critical temperature (2) lower than its critical temperature (3) higher than its Boyles temperature (4) lower than its Boyle's temperature

Short answer

Option (2) lower than its critical temperature.

Step-by-step solution

- Understand Critical Temperature

The critical temperature of a gas is the highest temperature at which it can be liquefied by pressure alone. Above this temperature, a gas cannot be liquefied regardless of the pressure applied.

- Analyze Each Option

Review each option in relation to the critical temperature:(1) Higher than its critical temperature: Above the critical temperature, a gas cannot be liquefied by pressure alone.(2) Lower than its critical temperature: Below the critical temperature, a gas can be liquefied by applying sufficient pressure.(3) Higher than its Boyle's temperature: Boyle's temperature is not directly related to the condition for liquefaction.(4) Lower than its Boyle's temperature: Similarly, Boyle's temperature does not determine the conditions for liquefaction.

- Select the Correct Option

From the analysis, the correct condition for a gas to be liquefied by pressure alone is when its temperature is lower than its critical temperature.

Key concepts

Gas Liquefaction

Gas liquefaction is the process of turning a gas into a liquid. This can be achieved by either lowering the temperature, increasing the pressure, or both. The main goal is to get gas molecules closer together, so they can form a liquid.
For a gas to liquefy under pressure alone, its temperature must be below its critical temperature. If the temperature is too high, no amount of pressure will liquefy the gas.
Think of molecules as people at a party. When the temperature is high, they have too much energy and stay far apart, like people dancing. Lowering the temperature calms them down, allowing them to move closer together, foreshadowing liquefaction.

Pressure and Temperature Relationship

The relationship between pressure and temperature is a core concept in thermodynamics and gas laws. When the temperature of a gas decreases, the molecules lose kinetic energy and come closer together, making it easier for the gas to liquefy with the application of pressure.

• Critical Temperature: This is the maximum temperature at which a gas can be liquefied by applying pressure alone.
• If the temperature is below this limit, applying enough pressure will force the gas to condense into a liquid.
• Above the Critical Temperature: No amount of pressure will be enough to turn the gas into a liquid.

Understanding this interplay is vital for many applications, from industrial gas liquefaction to basic scientific principles.

Boyle's Temperature

Boyle's temperature is a specific point where a real gas behaves most like an ideal gas. It's not directly related to liquefaction conditions.
Boyle's law states: For a fixed amount of gas at constant temperature, the volume is inversely proportional to the pressure exerted on the gas.
Boyle's temperature is crucial in understanding how gases behave over different temperature ranges, but it's not the same as the critical temperature which defines liquefaction conditions.

• Ideal Gas Behavior: At Boyle's temperature, compressing the gas does not change its volume like in real-world scenarios.
• Critical vs Boyle’s: Critical temperature determines the feasibility of liquefaction by pressure; whereas Boyle’s temperature is more about gas behavior under compression.