concept

critical point

A critical point is the specific temperature and pressure where distinct phases of matter become indistinguishable.
14 related articles · 4 formulas

Description

Imagine a kettle with boiling water. Normally, when water turns into steam, you can see bubbles and bubbling. But if you heat water under high pressure, you can reach a state where water and steam become completely indistinguishable — this is the critical point. At this point, liquid and gas merge into a single state, like a thick fog, but without a surface boundary. It's similar to how, in the morning, the air is so saturated with moisture that dew droplets and air merge into one whole.

History

The critical point was discovered by Charles Cagniard de la Tour in 1822, but systematically studied by Thomas Andrews in 1869. Andrews showed that for each gas there is a temperature above which it cannot be liquefied. In 1873, Johannes van der Waals proposed an equation of state for real gas that for the first time explained the existence of a critical point based on molecular forces. In the 20th century, Landau developed the theory of second-order phase transitions, and Wilson applied renormalization group to describe universal critical phenomena.

How it works

From a microscopic perspective, the critical point is the result of a balance between intermolecular attraction, which tends to condense the substance, and thermal motion, which tends to expand it. At the critical temperature, the attraction energy equals the thermal energy, and the phase boundary disappears. This is described by the van der Waals equation, which includes parameters a and b. At the critical point, compressibility tends to infinity, and the correlation length of fluctuations becomes macroscopic, leading to critical opalescence. In modern understanding, critical phenomena are universal and do not depend on system details, but are determined only by the dimensionality of space and the symmetry of the order parameter, as described by renormalization group theory.

Fun fact

Did you know that at the critical point, water can simultaneously wet and not wet the walls of the container? The difference between liquid and steam disappears, and surface tension vanishes, so the liquid stops forming droplets.

Concept graph →

Formulas

$$\frac{P_c v_c}{T_c} = \text{const}$$
Critical pressure, volume, and temperature have a constant ratio.
What is in the formula
P_cvariableCritical pressure — pressure pascal
v_cvariableCritical molar volume — molar volume cubic metre per mole
T_cvariableCritical temperature — temperature kelvin
\frac{p_cv_c}{t_c}={const} · 2512.19200
$$1 = U \chi(\omega)$$
Pairing instability occurs when eigenvalue reaches unity.
What is in the formula
UvariableEffective pairing interaction strength — coupling constant joule metre cubed
χvariablePair susceptibility (response function) — susceptibility per joule per metre cubed
ωvariableFrequency (Matsubara or real) — angular frequency per second
λ_{\max}(t_c)=1/u · 2607.02267
$$E_c \propto \frac{|m_a^2 - \omega_{\rm pl}^2|}{B_\perp g_{a\gamma}}$$
Critical energy where axion-photon oscillations become energy-independent.
What is in the formula
E_cvariableCritical energy — energy joule
m_avariableAxion mass — mass kilogram
ω_plvariablePlasma frequency — angular frequency radian per second
B_perpvariablePerpendicular magnetic field strength — magnetic field strength tesla
g_aγvariableAxion-photon coupling constant — coupling constant inverse gev
e_c\simeq2.5{гэв}(\frac{|m_a^2-ω_{\rmpl}^2|}{1{\rmнэв}})(\frac{b_\perp}{μ{г}})^{-1}(\frac{g_{aγ}}{10^{-11}{гэв}^{-1}})^{-1} · 2607.07158
$$p_1 p_2 = \frac{\gamma}{1+\gamma}$$
Product of pre- and post-shock pressures depends on adiabatic index.
What is in the formula
p_1variablePre-shock pressure — pressure pascal
p_2variablePost-shock pressure — pressure pascal
\gammavariableAdiabatic index (ratio of specific heats) — adiabatic index
p_{\rmpre}p_{\rmpost}=\frac{γ}{1+γ} · 2606.29607

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