Question

Is it possible to have water vapor at \(-10^{\circ} \mathrm{C} ?\)

Short answer

Answer: Yes, water vapor can exist at a temperature of -10°C under certain conditions, such as low pressure or when ice is sublimating at that temperature.

Step-by-step solution

Understand the phase diagram of water

A phase diagram is a graphical representation that shows the conditions, such as pressure and temperature, under which a substance can exist in different phases (solid, liquid, or gas). For water, the phase diagram helps us determine when it can exist as ice, liquid water, and water vapor.

Locate the given temperature on the phase diagram

We are given a temperature of \(-10^{\circ} \mathrm{C}\). Find this temperature on the horizontal axis of the phase diagram.

Determine the phase of water at this temperature

For the given temperature, \(-10^{\circ} \mathrm{C}\), locate the corresponding phase based on the phase boundaries shown in the diagram. From the phase diagram, we can see that at temperatures below \(0^{\circ} \mathrm{C}\) on the triple point line, water exists as a solid (ice).

Check if water vapor can exist

At \(-10^{\circ} \mathrm{C}\), we are in the solid phase (ice) region of the phase diagram. However, water can sublimate directly from the solid phase to the gaseous phase (water vapor) under certain conditions. The sublimation temperature of water at atmospheric pressure is below \(-10^{\circ} \mathrm{C}\). Therefore, it is possible to have water vapor at \(-10^{\circ} \mathrm{C}\) under certain conditions, such as low pressure or when ice is sublimating at that temperature.

Key concepts

Water Vapor at Sub-Zero Temperatures

One might assume that at sub-zero temperatures, water would be present only in solid form; however, water vapor can indeed exist even at these low temperatures. The presence of water vapor below the freezing point is a result of the water cycle's expansive reach, which encompasses a variety of environmental conditions.

At temperatures below freezing, under specific pressure conditions, water molecules can escape directly from the solid state (ice) into the gaseous state, bypassing the liquid phase entirely. This is observable in natural phenomena such as the formation of frost, which occurs when humid air comes into contact with a cold surface, causing water vapor to deposit as frost without first becoming liquid water.

• The phase diagram of water is a crucial tool in understanding how water can exist as a vapor below freezing temperatures.
• Sublimation, the process through which solid ice turns directly into vapor, is key to the presence of water vapor at sub-zero temperatures.

This illustrates that even when we're in the grip of winter's cold, the air around us can still hold moisture, albeit at reduced levels compared to warmer conditions.

Sublimation of Ice

Sublimation is a fascinating thermodynamic process where ice transforms directly into water vapor without passing through the liquid phase. It's particularly common in areas where low pressure and low humidity prevail, such as in high-altitude or polar environments.

The process of sublimation is not only fundamental to understanding various natural phenomena but also plays a crucial role in certain industries. For example, 'freeze-drying' is a technique that utilizes sublimation to preserve food and other perishables by rapidly freezing them and then applying a vacuum to remove the ice as vapor. This results in a product that is light, less susceptible to spoiling, and convenient for transportation and storage.

• Atmospheric conditions greatly influence the rate of sublimation: low temperature and low pressure favor this process.
• Sublimation is an endothermic transition, meaning it requires energy to proceed, taking in heat from its surroundings.

Thermodynamics of Phase Changes

Understanding the thermodynamics of phase changes is essential in predicting how a substance like water will behave under varying conditions of temperature and pressure. Each phase change--whether melting, freezing, vaporization, condensation, or sublimation--involves energy transfer.

During a phase change, energy is absorbed or released by the substance, but its temperature remains constant. For instance, when ice melts, it absorbs heat but maintains a temperature at the melting point until the phase change is complete. Conversely, when water vapor condenses, it releases heat but remains at the condensing temperature until it completely transforms into liquid.

• The amount of energy involved in a phase change is quantified by the enthalpy of transition, such as the enthalpy of sublimation for ice transforming into vapor.
• Phase diagrams, which plot temperature against pressure, enable us to determine the conditions under which a substance will undergo specific phase transitions.

Thermodynamics offers insights into the energy changes that occur and the equilibrium between phases, which can dictate whether you'll see ice, water, or vapor at a given set of environmental conditions.