Understanding the Triple Point of Water

The triple point of water is a specific temperature and pressure at which the three phases of water — solid (ice), liquid (water), and gas (water vapor) — coexist in thermal equilibrium.

Calculating Degree of Freedom using Gibbs' Phase Rule

To determine the degree of freedom of a system at equilibrium, we use Gibbs' Phase Rule. The rule is given by the formula:

\( F = C - P + 2 \)

Where:

• \( F \) is the degree of freedom (the number of independent variables, such as temperature or pressure, that can be varied without changing the number of phases in equilibrium).
• \( C \) is the number of components in the system.
• \( P \) is the number of phases present in the system.

Applying Gibbs' Phase Rule at the Triple Point

For the system at the triple point of water:

• The system consists of pure water, so there is only one chemical constituent. Thus, the number of components \( C = 1 \).
• At the triple point, three phases of water (ice, liquid water, and water vapor) coexist simultaneously. Thus, the number of phases \( P = 3 \).

Now, we can substitute these values into Gibbs' Phase Rule:

\( F = C - P + 2 \)

\( F = 1 - 3 + 2 \)

\( F = -2 + 2 \)

\( F = 0 \)

Interpreting the Degree of Freedom

The calculated degree of freedom at the triple point of water is \( F = 0 \). This means that there are no independent variables (like temperature or pressure) that can be changed without causing one of the phases to disappear. In other words, the temperature and pressure at the triple point of a pure substance like water are fixed and unique constants.

Therefore, the degree of freedom at the triple point of water is 0.