Question

Sketch the cooling curves of water from about ${110}^{\circ }\mathrm{C}$ to about $-{10}^{\circ }\mathrm{C}$. How would you also show the formation of supercooled liquid below $0^{\circ }\mathrm{C}$ that then freezes to ice? The pressure is at 1 atm throughout the process. The curves need not be drawn quantitatively

Short answer

Sketch cooling from 110°C to -10°C with liquid-vapor and liquid-solid transitions at 100°C and 0°C; include supercooling below 0°C.

Step-by-step solution

Understanding the Problem

We need to sketch the cooling curve of water as it transitions from a high temperature of 110°C down to -10°C. Key phases include the vapor cooling to water, water cooling and freezing into ice, and potentially observing supercooling where liquid water cools below 0°C without freezing immediately.

Sketching the Cooling of Vapor to Liquid

Start the cooling curve at 110°C. As water vapor cools, it will condense into liquid water at 100°C. Represent this phase change by a horizontal line at 100°C, indicating heat release without a temperature change, as latent heat of vaporization is being removed.

Cooling of Liquid Water

After reaching the liquid phase at 100°C, continue the cooling curve with a diagonal line downwards as water temperature decreases from 100°C to 0°C. This segment represents the cooling of liquid water.

Formation of Ice

At 0°C, draw another horizontal line indicating the phase change from liquid to solid. This is where water begins to freeze, releasing latent heat of fusion without a temperature change.

Supercooling and Freezing Below 0°C

To show supercooling, extend the liquid water line below 0°C without a phase change. Then, depict a sudden vertical drop to complete the phase change to ice once the liquid eventually begins to crystallize, which can sometimes occur spontaneously if no nucleation sites are present to initiate freezing.

Final Cooling of Ice

From the point where the water freezes, continue with a diagonal line downward representing the cooling of the solid ice from 0°C to -10°C.

Key concepts

Phase Changes

Understanding phase changes is crucial when sketching cooling curves of substances like water. Phase changes occur when matter transitions between solid, liquid, and gas states. For water, these transitions include melting, freezing, condensation, and vaporization.

When plotting a cooling curve, horizontal lines represent phase changes. For instance, water condenses from vapor to liquid at 100°C, illustrated by the latent heat of vaporization. During this process, heat is removed without a temperature drop, resulting in a flat line on the curve.

• Condensation (vapor to liquid)
• Freezing (liquid to solid)

These transitions are key in understanding how substances release or absorb energy when cooling down.

Supercooling

Supercooling is an intriguing phenomenon where a liquid cools below its freezing point without solidifying. When water reaches below 0°C without becoming ice, it remains in a liquid state until it spontaneously freezes.

This can occur when there are no impurities or nucleation sites, which are usually required to initiate the phase transition to a solid. In a cooling curve, supercooling is represented by a line extending below 0°C while still in the liquid phase. Eventually, a sudden shift occurs as the supercooled water abruptly freezes.

• No immediate phase change under 0°C
• Sudden crystallization once it begins freezing

Such behavior is crucial for understanding atypical reactions during cooling processes.

Temperature Transitions

Temperature transitions are essential on a cooling curve as they show the change in heat without altering the substance's state. During these segments:

• After condensation, liquid water cools from 100°C to 0°C.
• After the freezing point is reached, ice cools from 0°C to -10°C.

These parts of the curve are represented by sloped lines as the temperature directly decreases.
This part of the curve illustrates the removal of sensible heat, where the substance's kinetic energy lessens and the particles slow down.

Heat of Vaporization

The heat of vaporization is the energy required for a liquid to transition to a gas at a constant temperature. For water, it is the energy removed when vapor condenses into a liquid, highlighted by the horizontal line at 100°C on a cooling curve.

This heat removal does not change the temperature since the energy goes into changing the state rather than heating the substance. Understanding this concept of latent heat removal is crucial when exploring phase changes.

• Represents energy absorbed or released
• Occurs during the vapor to liquid transition

Recognizing the heat of vaporization is critical for comprehending how energy exchange affects matter states.

Heat of Fusion

The heat of fusion refers to the energy necessary to transition a solid to a liquid, and conversely, the heat released when liquid water freezes into ice. At 0°C, this energy removal occurs without a temperature change.

Drawing a horizontal line at 0°C on the cooling curve signals the phase change from liquid to solid. During this, the latent heat of fusion is removed. No temperature decrease is noted during the transition.

• Energy required for melting or freezing
• Illustrated by phase change without temperature fluctuation

Understanding the heat of fusion is vital for interpreting the energy dynamics during solid-liquid transitions.