\(\alpha \)- sulfur converts to \(\beta \)-sulfur above 369K. This temperature is known as:

Transition temperature

The correct answer is option 4. Transition temperature.

Let us delve into the concept of the transition temperature and its significance in the context of sulfur allotropes:

Sulfur can exist in different allotropes, each with distinct crystalline structures and properties. The two main allotropes are:

α-Sulfur (Rhombic Sulfur):

It has a rhombic crystal structure and is stable at lower temperatures.

Color: Typically a yellow solid.

Stability: Stable at temperatures below 369 K.

β-Sulfur (Monoclinic Sulfur):

It has a monoclinic crystal structure and is stable at higher temperatures.

Color: Also yellow, but with a different crystalline form.

Stability: Becomes stable above 369 K.

Transition temperature is a specific temperature at which one phase or form of a substance converts into another. For sulfur, this is the temperature at which the two allotropes (α and β) interconvert.

At 369 K (96°C), sulfur undergoes a phase transition from the rhombic (α) form to the monoclinic (β) form. This temperature is known as the transition temperature because it marks the point where the stability of the two allotropes changes.

Phase Transition: In materials science and chemistry, a phase transition is a transformation in the physical state or crystal structure of a material. In the case of sulfur, it involves a change in the crystalline arrangement of sulfur atoms, not a change in the chemical composition.

Other Temperatures and Concepts

Critical Temperature: The temperature above which a substance cannot be liquefied, regardless of the pressure applied. It is relevant to gases and their phase transitions to liquids, not to solid allotropes.

Boyle's Temperature: The temperature at which a real gas exhibits ideal gas behavior over a range of pressures. It is a concept related to gas behavior, not phase transitions in solids.

Kelvin Temperature: A unit of temperature measurement on the Kelvin scale, which starts from absolute zero. It does not specify a phase transition; it’s simply a scale for measuring temperature.

Summary

The transition temperature of 369 K is significant because it represents the specific temperature at which α-sulfur transforms into β-sulfur. This transition reflects a change in the crystalline structure of sulfur rather than a change in chemical composition or behavior as seen in other temperature-related phenomena.

By understanding the concept of transition temperature, we can better grasp how materials like sulfur change their properties based on temperature and how these changes can impact their applications in various scientific and industrial contexts.