When a sharp glass edge is heated up to its melting point in a flame, it becomes smooth due to a process called surface tension. Surface tension is the property of liquids that causes their surfaces to behave like a stretched elastic membrane, minimizing surface area and forming spherical shapes. This phenomenon arises from the cohesive forces between molecules in the liquid.

Here's how the process unfolds:

1. Heating the Glass: When the sharp glass edge is heated in a flame, the temperature of the glass increases. As the temperature rises, the kinetic energy of the glass molecules increases, causing them to vibrate more vigorously. Eventually, the temperature reaches the melting point of the glass, causing the glass to transition from a solid to a liquid state.

2. Surface Tension Effect: As the glass melts, the cohesive forces between the glass molecules become dominant. These forces tend to minimize the surface area of the liquid glass. As a result, the liquid glass adopts a spherical shape, pulling inwards at the sharp edges.

3. Smoothing Effect: As the liquid glass retracts and forms a smooth, rounded surface, any sharp edges or protrusions are gradually smoothed out. This process occurs due to the surface tension pulling the liquid glass inward, effectively rounding off any irregularities or sharp features.

In summary, the property of surface tension in liquids is responsible for the phenomenon of a sharp glass edge becoming smooth when heated up to its melting point. Surface tension causes the liquid glass to minimize its surface area, resulting in the rounding off of sharp edges and the formation of a smooth surface.

The boundary between the liquid phase and the gaseous phase disappears when a liquid is heated up to its critical temperature in a closed vessel due to the process of reaching the critical point. At the critical temperature, the distinction between the liquid and gas phases becomes indistinguishable, and the substance exists in a state known as the supercritical fluid state.

Here's why this occurs:

1. Critical Temperature: The critical temperature (Tc) is the temperature above which a substance cannot exist in the liquid phase, regardless of pressure. At this temperature, the distinction between the liquid phase and the gas phase disappears, and the substance transitions into a supercritical fluid state.

2. Critical Pressure: The critical pressure (Pc) is the pressure required to liquefy a gas at its critical temperature. Below the critical temperature, increasing pressure can cause a gas to liquefy. However, above the critical temperature, no amount of pressure can cause liquefaction.

3. Supercritical Fluid State: When a substance is heated above its critical temperature in a closed vessel, it enters the supercritical fluid state. In this state, the substance exhibits properties of both a liquid and a gas. It has the density of a liquid and the ability to diffuse through materials like a gas. The boundary between the liquid phase and the gas phase becomes blurred, and the substance behaves as a homogeneous fluid.

In this situation, the substance will exist in the supercritical fluid state. It will not have distinct liquid and gas phases, as they merge into one homogeneous phase. The substance will exhibit properties of both liquids and gases, such as high diffusivity and solubility, making it useful in various industrial processes such as extraction, chromatography, and chemical reactions.

Increasing the temperature of a liquid affects the intermolecular forces operating between its particles in several ways:

1. Increased Kinetic Energy: As the temperature of a liquid increases, the average kinetic energy of its particles also increases. This increased kinetic energy causes the particles to move faster and collide with each other more frequently.

2. Weakening of Intermolecular Forces: Intermolecular forces, such as van der Waals forces, hydrogen bonding, and dipole-dipole interactions, are responsible for holding the particles of a liquid together. When the temperature of the liquid increases, the increased kinetic energy of the particles overcomes these intermolecular forces more easily. As a result, the intermolecular forces weaken, leading to a decrease in the cohesive forces holding the liquid together.

3. Increased Thermal Motion: Higher temperatures lead to greater thermal motion of the particles within the liquid. This increased thermal motion disrupts the ordered arrangement of particles and reduces the tendency for the particles to remain in close proximity to each other.

4. Expansion of Volume: The increased kinetic energy of the particles at higher temperatures causes the volume of the liquid to expand. This expansion results from the particles moving farther apart from each other as they gain energy, leading to a decrease in the density of the liquid.

Regarding the viscosity of a liquid, increasing the temperature typically leads to a decrease in viscosity. This is because higher temperatures result in weaker intermolecular forces, as discussed above. Weaker intermolecular forces allow the liquid particles to move more freely past each other with less resistance, reducing the internal friction within the liquid and hence its viscosity.

In summary, increasing the temperature of a liquid weakens the intermolecular forces operating between its particles, leading to reduced cohesion and increased thermal motion. As a result, the viscosity of the liquid decreases as its temperature increases.

The intermolecular forces present in the given liquids are:

1. Water (H2O): Hydrogen bonding
2. Hexane (CH3CH2CH2CH2CH2CH3): London dispersion forces (van der Waals forces)
3. Glycerine (CH2OHCH(OH)CH2OH): Hydrogen bonding and London dispersion forces

Now, let's arrange them in increasing order of their viscosities:

1. Hexane (CH3CH2CH2CH2CH2CH3): This liquid primarily experiences London dispersion forces, which are relatively weaker compared to hydrogen bonding. Therefore, it typically has the lowest viscosity among the given liquids.

2. Water (H2O): Water experiences hydrogen bonding, which is stronger than London dispersion forces. Thus, it has a higher viscosity compared to hexane.

3. Glycerine (CH2OHCH(OH)CH2OH): Glycerine experiences both hydrogen bonding and London dispersion forces. Hydrogen bonding contributes significantly to the viscosity of glycerine, making it the most viscous among the given liquids.

Reason for the assigned order: Viscosity is primarily determined by the strength of intermolecular forces. Hexane has weaker intermolecular forces (London dispersion forces) compared to water (hydrogen bonding) and glycerine (hydrogen bonding and London dispersion forces), resulting in lower viscosity. Water, with its strong hydrogen bonding, has a higher viscosity than hexane. Glycerine, which exhibits both hydrogen bonding and London dispersion forces, experiences stronger intermolecular forces overall, leading to the highest viscosity among the given liquids.