At what phase or phases could water exist at 4.579mm pressure and 0.0098°C

Explanation

The triple point of water is defined by the following conditions:

Under these specific conditions, water can simultaneously exist as ice (solid), liquid water, and water vapor (gas).

Important Points

• The triple point is a unique thermodynamic condition specific to each substance where three phases coexist in equilibrium.
• For water, this occurs at a pressure of 4.579 mmHg and a temperature of 0.0098°C.

Therefore, under the specified conditions of 4.579 mm pressure and 0.0098°C, water exists in solid, liquid, and gas phases.

Explanation of the Triple Point of Water

The triple point of water is a unique concept in thermodynamics. It refers to the specific combination of temperature and pressure at which water exists simultaneously in all three of its phases: solid, liquid, and gas. This condition is extremely specific and forms the basis for calibrating thermometers and defining temperature scales.

Temperature and Pressure

The triple point of water occurs at an exact temperature of 0.01°C (273.16 K) and a pressure of 611.657 pascals (0.00604 atm). This precise condition can be expressed mathematically as:

Importance in Thermodynamics

1. Thermodynamic Equilibrium: At the triple point, water's three phases (ice, liquid water, and water vapor) exist in a state of thermodynamic equilibrium.
2. Calibration: The precise values of temperature and pressure at the triple point of water are used to define the Kelvin temperature scale.
3. Critical Phenomenon: It serves as a fundamental fixed point from which other thermodynamic properties can be derived.

Practical Applications

1. Metrology: Used in the precise calibration of thermometric instruments.
2. Scientific Research: Provides a benchmark for studies involving water's phase transitions.

Understanding the triple point of water is crucial for both scientific research and practical applications like thermometer calibration and climate studies.

Explanation

The concept of the coexistence of phases in thermodynamics refers to the condition under which different phases (solid, liquid, gas) of a substance exist together at equilibrium. This typically occurs at specific combinations of pressure and temperature, known as phase boundaries.

Phase Diagrams

A phase diagram is a graphical way to depict the conditions under which distinct phases occur and coexist at equilibrium. These diagrams usually have pressure on the y-axis and temperature on the x-axis. Points or lines on the diagram where two or more phases coexist are called coexistence curves.

Gibbs Free Energy

The equilibrium between phases is determined by the minimization of the Gibbs free energy $G$. For two phases to coexist, their Gibbs free energies must be equal:

Clausius-Clapeyron Equation

The Clausius-Clapeyron equation describes the phase boundary between two phases (such as solid and liquid or liquid and gas). It is given by:

Here:

• $\frac{dP}{dT}$ is the slope of the coexistence curve.
• $\Delta S$ is the change in entropy during the phase transition.
• $\Delta V$ is the change in volume during the phase transition.

Triple Point

A special point on a phase diagram is the triple point, where all three phases coexist in equilibrium. For water, the triple point is at a precise temperature of 273.16 K and a pressure of 611.657 Pa.

Key Insights

• Equilibrium Conditions: Coexistence implies that the thermodynamic potentials are equal for the phases in equilibrium.
• Phase Boundaries: The lines or curves separating single-phase regions are where phases can coexist.
• Triple Point: A unique point delineating conditions for the coexistence of three phases.

Understanding the coexistence of phases helps in various scientific and industrial processes, including the design of refrigeration systems, the study of material properties, and the synthesis of new compounds.