# Critical Point | Constants, Determination, Critical Phenomena |

## Critical Point.

The curve representing the variation of volume and pressure at constant temperature is called isotherm.

A gas can be liquified by increasing pressure and decreasing temperature. At a temperature and pressure, a gas changes to vapor. It is called the critical state of the gas. The point representing this state in an isotherm is called critical point, e.g., F is a critical point in the isotherm CO2 at 31 °C.

### Experimental Determination of Critical Constants.

Critical temperature and pressure can be measured with Cagniard’s apparatus. It is a U-shaped glass tube with a bulb at the lower end. The liquid is contained in the bulb and the rest of the apparatus is filled with mercury and the upper and of the bulb is sealed leaving a little air in it. The temperature of the bulb is raised gradually. A point reaches when the liquid disappears and a homogeneous mixture of vapors and air is left in it. On cooling this mixture, a mist first forms and the liquid appear quickly.

The mean of the temperature of the disappearance and reappearance of the liquid in the bulb is critical temperature. The pressure read on the manometer is “critical pressure”.

### Determination of Critical Volume.

Amagat devised a method to determine the critical volume. It consists of measuring the densities of liquid and its vapors near the critical point. These two densities are plotted against the temperature. When extended, these curves meet at the critical temperature, because at this temperature the densities of liquid and vapor become equal. The mean values of densities of liquid and vapor are plotted and we gat CD which passed through C, the critical temperature. The intersection of CD and ABC at C gives the critical density. From this, the critical volume can be calculated.

### Critical Phenomena and Critical State.

The essential conditions for the liquefaction of gas were discovered by T. Andrew. He made the determination with CO2 at various temperatures.

1. At 50 °C, CO2 obeys gas law, i.e., Boyle’s Law.
2. At 31.1 °C, the Isotherm shows a break at F and a decrease in volume for a small change pressure.
3. At 21 °C, the curve remains horizontal at YZ and the gas changes to liquid at Y at the same pressure although the volume change.

At point F, there exists an equilibrium between the gas and liquid, and it exists in a vapor state. “The state of a gas when it is present in vapor state at definite temperature and pressure is called the critical state“.

The point F is called a critical point and the isotherm passing through it is called critical isotherm.