Solid water (ice) is slowly warmed from a very low temperature. (a) What minimum external pressure p1 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 < p1.

Verified step by step guidance

1. Understand the phase diagram of water: Water has a unique phase diagram where the solid-liquid boundary line has a negative slope. This means that increasing pressure can lower the melting point of ice.
2. Identify the triple point of water: The triple point is the condition under which all three phases (solid, liquid, and gas) coexist in equilibrium. For water, this occurs at a pressure of 611.657 pascals and a temperature of 0.01°C.
3. Determine the minimum pressure for melting: The minimum external pressure p1 required for ice to melt directly into liquid water is the pressure at the triple point. Below this pressure, ice will sublimate directly into vapor without melting.
4. Describe phase transitions for p < p1: If the applied pressure p is less than p1, as the ice is warmed, it will undergo sublimation, transitioning directly from solid to gas without passing through the liquid phase.
5. Summarize the sequence of phase transitions: For p < p1, the sequence is solid (ice) to gas (vapor) upon warming. For p ≥ p1, the sequence is solid (ice) to liquid (water) to gas (vapor) as temperature increases.

Key Concepts

Phase Transitions

Phase transitions refer to the transformation of a substance from one state of matter to another, such as from solid to liquid. This process occurs when the temperature and pressure conditions reach specific thresholds, known as the melting point for solid to liquid transitions. Understanding these conditions is crucial for predicting the behavior of substances under varying external pressures.

Pressure and Melting Point

The melting point of a substance can be influenced by external pressure. For ice, increasing pressure can lower the melting point, allowing it to transition to liquid at lower temperatures. The minimum external pressure p1 required for melting indicates the threshold above which ice will melt upon warming. Below this pressure, ice may undergo sublimation directly to vapor without melting.

Sublimation

Sublimation is the phase transition where a solid turns directly into a gas without passing through the liquid phase. This occurs under conditions where the pressure is below the substance's triple point, such as when p < p1 for ice. Understanding sublimation is essential for predicting the sequence of phase transitions when ice is warmed under low pressure conditions.