Solid water (ice) is slowly warmed from a very low...

Solid water (ice) is slowly warmed from a very low temperature. (a) What minimum external pressure $p_{1}$ must be applied to the solid if a melting phase transition is to be observed? Describe the sequence of phase transitions that occur if the applied pressure $p$ is such that $p<p_{1}$ . (b) Above a certain maximum pressure $p_{2},$ no boiling transition is observed. What is this pressure? Describe the sequence of phase transitions that occur if $p_{1}<p<p_{2}$

Solid water (ice) is slowly warmed from a very low temperature. (a) What minimum external pressure $p_{1}$ must be applied to
the solid if a melting phase transition is to be observed? Describe
the sequence of phase transitions that occur if the applied pressure $p$ is such that $p<p_{1}$ . (b) Above a certain maximum pressure $p_{2},$ no
boiling transition is observed. What is this pressure? Describe the
sequence of phase transitions that occur if $p_{1}<p<p_{2}$

Key Concepts

Sublimation versus Melting

Sublimation refers to the direct transition from solid to vapor without passing through the liquid phase, which occurs at pressures below the triple point. Melting, on the other hand, is the transition from solid to liquid and only occurs when the external pressure is above the triple point. Recognizing the difference between these two types of phase transitions is essential for predicting the sequence of events under different pressure conditions.

Vapor Pressure and Boiling Point

The concept of vapor pressure is integral to understanding boiling. A liquid boils when its vapor pressure equals the external pressure. There exists a maximum external pressure above which the vapor pressure of the liquid can never reach the applied pressure, meaning that boiling transitions no longer occur. This concept is key to understanding the upper pressure limit for the liquid?vapor transition.

Clausius-Clapeyron Relation

The Clausius-Clapeyron relation describes how the pressure and temperature at which phase transitions occur are related. It is especially useful for determining the slopes of the phase boundaries on a phase diagram, which in turn explains how changes in external pressure can shift the conditions for melting, boiling, or sublimation.

Triple Point

The triple point is a unique condition of temperature and pressure at which a substance can coexist in three phases—solid, liquid, and vapor—in equilibrium. For water, this concept is crucial because it marks the minimum pressure required for melting to occur rather than sublimation, and it separates the solid-vapor transition from the solid-liquid transition.

Phase Diagram

A phase diagram is a graphical representation that shows the stability regions of different phases of a substance as functions of temperature and pressure. It helps in understanding the conditions under which a substance can exist as a solid, liquid, or gas, and also depicts the boundaries where phase transitions occur.

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