Clausius- Clapeyron Equation

An equation governing phase transitions of a substance, in which p is the pressure, T is the temperature at which the phase transition occurs, ΔH is the change in heat content (enthalpy), and ΔV is change in the volume during the transition heat of Vaporization is generally related with the Clausius-Claperon equation. The Clausius–Clapeyron relation is the way of by which we can characterize a discontinuous phase transition among 2 phases of matter. On a pressure–temperature  line separating the 2 phases is called as the coexistence curve. The Clausius–Clapeyron relation provides the slope of this curve.

As the temperature and pressure are constant at the time of phase change, derivative of the pressure with respect to temperature is not a function of the specific volume. When the transition is to a gas phase, the last specific volume can be several times the size of the initial specific volume. A natural approximation is to replace Δv with v². Furthermore, at low pressures, gas phase can be approximated by the ideal gas law, so that v² = vgas = RT / P, here R is mass specific gas constant. This equation is taken in used to find out the relationships among temperature and pressure for the phase change boundaries. Volume and entropy and changes because of the phase change are orthogonal to plane of the drawing. Phase changes, such as the conversion of liquid water to steam, provide an important example of the system in which there exists a large change in internal energy with volume at constant temperature. Assume that the cylinder contains both water and steam in equilibrium with each other at pressure P, and the cylinder is held at constant temperature T. The pressure remains equal to the atmospheric water vapor. The concentration of water vapour in atmosphere cannot vary freely. Instead, it is determined by the temperature of the lower atmosphere and surface through a physical relationship known as the Clausius-Clapeyron equation. Chemists often use this equation to estimate the vapour pressures of pure solids or liquids.