Question

The degree of freedom when ice, water, and water vapour co-exist in equilibrium is

• A. 1
• B. 3
• C. 0
• D. -1

Hint:

The triple point of water occurs at 0.01°C and 0.006 atm, where ice, liquid water, and water vapour exist in equilibrium.

Answer 1

The Correct Option is C

The degree of freedom (F) in a system is calculated using Gibbs' phase rule, given by: \[ F = C - P + 2 \] where: - \( C \) = Number of components in the system, - \( P \) = Number of phases present, - The constant 2 represents the two variables (temperature and pressure) that define the system. Step 1: Identifying Parameters - The system consists of water in three phases: solid (ice), liquid (water), and gas (vapour), so \( P = 3 \). - The only component in the system is \( H_2O \), so \( C = 1 \).

Step 2: Applying Gibbs' Phase Rule \[ F = 1 - 3 + 2 = 0. \]

Step 3: Conclusion Since \( F = 0 \), the system is invariant, meaning that at the triple point, temperature and pressure are fixed, and no degree of freedom remains. Thus, the correct answer is (C) 0.