## Chemistry

In chemistry, a **critical point** is the conditions (temperature, pressure) at which the liquid state of the matter ceases to exist. As a liquid is heated, its density decreases while the density of the vapor being formed increases. The liquid and vapor densities become closer and closer to each other until the critical temperature is reached where the two densities are equal and the liquid-gas line or phase boundary disappears.

*A typical phase diagram.*

In the above diagram, the phase boundary between liquid and gas does not continue indefinitely. Instead, it terminates at a point on the phase diagram called the **critical point**. This reflects the fact that, at extremely high temperatures and pressures, the liquid and gaseous phases become indistinguishable. In water, the critical point occurs at around 647 K (374 °C or 705 °F) and 22.064 MPa.

Critical variables are useful for rewriting a varied equation of state into one that applies to all materials.

## Physics

In physics, it is sometimes taken to mean the point of a second order phase transition.

According to Renormalization Group Theory , the defining property of criticality is that the natural lengthscale characteristic of the structure of the physical system, the so-called correlation length ξ, becomes infinite. There are also lines in phase space along which this happens: these are Critical lines .

## Mathematics

In mathematics, a **critical point** (or **critical number**) is a point on the domain of a function where the derivative is infinite, undefined, or equal to zero. The last kind is a stationary point.

In higher dimensions, and for functions of several variables, this concept becomes a point where the rank of the derivative (Jacobian matrix) is not maximal (see submersion).

Last updated: 10-18-2005 03:50:45