Question

The figure shows a section of the phase boundary separating the vapour (1) and liquid (2) states of water in the P-T plane. Here, C is the critical point. μ₁. ν₁ and s₁ are the chemical potential, specific volume and specific entropy of the vapour phase respectively, while μ₂. ν₂ and s₂ respectively denote the same for the liquid phase. Then

• A. μ₁ = μ₂ along AB
• B. ν₁ =ν₂ along AB
• C. s₁ =s₂ along AB
• D. ν₁ =ν₂ at the point C

Answer 1

The Correct Option is A, D

The question involves understanding the phase boundary of water on a pressure-temperature (P-T) plane, specifically between vapour and liquid phases. To solve this, we need to understand phase equilibrium concepts.

In a phase equilibrium situation, such as the vapour-liquid equilibrium along the boundary line AB in the P-T diagram, certain thermodynamic properties are equal. Let's evaluate each statement:

1. μ₁ = μ₂ along AB: This is correct. At equilibrium along a phase boundary, the chemical potential (μ) is equal for both phases. This ensures that there is no net transfer of matter from one phase to another. Thus, μ₁ = μ₂ along AB.
2. ν₁ = ν₂ along AB: This is incorrect. The specific volume (ν) of a vapour is not typically equal to that of a liquid at phase equilibrium. Thus, this option is incorrect.
3. s₁ = s₂ along AB: This is incorrect. During phase changes, the specific entropy (s) is different between the vapour and liquid phases due to the heat transfer involved in the phase change. Thus, s₁ is not equal to s₂ along AB.
4. ν₁ = ν₂ at point C: This is correct at the critical point (C). At the critical point of a substance, the properties of the liquid and vapour phases become indistinguishable, including specific volume. Thus, ν₁ = ν₂ at point C.

Therefore, the correct answers are:

• μ₁ = μ₂ along AB
• ν₁ = ν₂ at point C

This analysis is consistent with the principles of phase equilibrium and critical points in thermodynamics.