Which option is not correct for a liquid to vapour phase transition at critical point?a)Entropy is continuous at transition pointb)Chemical potential is continuous at transition pointc)Isothermal compresibility is discontinuous at transition pointd)Specific heat diverges at transition pointCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Introduction:
The liquid to vapor phase transition at the critical point is a special case where the liquid and vapor phases become indistinguishable from each other. At this point, several properties undergo significant changes. In this response, we will discuss the options provided and explain why option 'D' is the correct answer.

Explanation:

Entropy is continuous at transition point:
Entropy is a measure of the disorder in a system. At the critical point, the liquid and vapor phases merge, resulting in a continuous increase in disorder. Therefore, entropy is continuous at the transition point.

Chemical potential is continuous at transition point:
Chemical potential is a measure of the energy required to add one more particle to a system. At the critical point, the liquid and vapor phases coexist, and the chemical potential remains constant, indicating the equilibrium between the two phases. Therefore, chemical potential is continuous at the transition point.

Isothermal compressibility is discontinuous at transition point:
Isothermal compressibility is a measure of how much a substance can be compressed under constant temperature conditions. At the critical point, the densities of the liquid and vapor phases become identical, and the compressibility undergoes a sudden change. Therefore, isothermal compressibility is discontinuous at the transition point.

Specific heat diverges at transition point:
Specific heat is a measure of the amount of heat required to raise the temperature of a substance. At the critical point, the substance requires an infinite amount of heat to change its phase completely. This is because the liquid and vapor phases merge, and the heat capacity becomes extremely high. Therefore, specific heat diverges at the transition point.

Conclusion:
Among the given options, the correct answer is option 'D' - specific heat diverges at the transition point. This is because the specific heat becomes extremely high at the critical point due to the merging of the liquid and vapor phases.

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