Questions: Critical Point Phenomena

Question 1

A substance is held at temperature T = 1.2 T_c. What happens if you compress it isothermally to very high pressure?

• A. It liquefies once pressure exceeds a critical threshold
• B. It remains in a single supercritical phase, becoming denser but never crossing a phase boundary
• C. It undergoes a first-order phase transition to liquid
• D. It separates into coexisting liquid and gas regions

Answer: (B)

Above T_c, there is no liquid-vapor phase boundary — the substance cannot be liquefied regardless of applied pressure. It becomes increasingly dense and liquid-like, but properties change continuously with no discontinuity. This is the defining feature of the supercritical state. The tempting wrong answer (A) reflects the misconception that high pressure always produces a liquid; that is only true below T_c.

Question 2

Critical opalescence — the milky-white appearance of a fluid near its critical point — occurs because:

• A. The substance undergoes a color-producing phase transition
• B. Density fluctuations at length scales comparable to visible-light wavelengths scatter light strongly
• C. The refractive index changes abruptly as the two phases begin to merge
• D. Liquid and gas layers form optical interference patterns

Answer: (B)

Near the critical point, the compressibility diverges and the correlation length ξ grows to macroscopic scales. This means density fluctuations occur on all length scales simultaneously, including those comparable to the wavelength of visible light. These fluctuations scatter light intensely (Rayleigh/Mie scattering), making the fluid appear milky-white. It is a direct signature of the diverging correlation length, not a phase transition color change.

Question 3

Above the critical temperature, applying sufficient pressure will typically cause a substance to liquefy.

• T. True
• F. False

Answer: False

This is the defining property of the critical point. Above T_c, there is no phase boundary between liquid and vapor — the two phases have merged into a single supercritical phase. No amount of pressure will cause liquefaction; you can only compress the supercritical fluid continuously. Liquefaction by isothermal compression is only possible below T_c.

Question 4

At the critical point on a P-V diagram, the isotherm simultaneously has zero slope and an inflection point.

• T. True
• F. False

Answer: True

This is the mathematical definition of the critical point: (∂P/∂V)_T = 0 (zero slope) and (∂²P/∂V²)_T = 0 (inflection point) are satisfied simultaneously. The first condition means liquid and gas are equally compressible; the second means there is no longer any sense in which one phase is denser than the other. These two conditions together uniquely determine T_c, P_c, and V_c for the van der Waals equation.

Question 5

Why can the properties of a supercritical fluid be 'tuned' continuously by adjusting temperature and pressure, while this is not possible for a substance below T_c?

Model answer: Below T_c, liquid and vapor are separated by a first-order phase boundary. Crossing that boundary causes discontinuous jumps in density, enthalpy, and other properties. Above T_c, the phase boundary no longer exists — properties (density, viscosity, diffusivity, solvent power) vary smoothly and continuously with T and P. This is why supercritical CO₂ can be dialed in as a gentle or aggressive solvent simply by adjusting conditions, with no abrupt transitions.

The tunability is a direct consequence of the absence of a phase boundary above T_c. Industrial applications like coffee decaffeination and pharmaceutical extraction exploit exactly this: supercritical CO₂ properties can be finely adjusted without ever crossing a discontinuous phase transition.