Phase Change Diagram With Equations

The slope of the phase line quickly reveals the equilibrium solutions and type of equilibration process. We use a line of slope 1 which passes through the origin to help us see how the time path will evolve.

Thermodynamics Chapter 2

At higher altitudes the air pressure is lower.

Phase change diagram with equations. Phase plane diagrams of difference equations tanya dewland jerome weston and rachel weyrens. You should know all of the variables in the equation except one. By analyzing phase plane diagrams of di erence equa tions are if we are modeling decay or growth convergence stability.

Phase diagram for water for most water pressures and temperatures that are relevant to the atmosphere. Identify the energy source and write it on the left hand side of the equation. Liquid to gas phase change.

The equilibrium vapor pressure between water vapor to the right of the line and liquid water to the left of the line as calculated by the clausius clapeyron equation. This diagram allows us to explain strange phenomena such as why water boils at a lower temperature at higher altitudes for example. T this temperature any heat added to the water goes breaking the hydrogen bonds between the water molecules as liquid water is converted to steam.

To solve energy problems you can generally follow these steps. Identify all the changes in temperature and in phase and put them on the right hand side. Using a heating curve and and example of the cacluationns needed to determine how much anargey is needed to heat a substance as it goes through phase changes.

A phase diagram indicates the sign of xt for a representative collection of values of x. To construct such a diagram plot the function f which gives the value of x. An equilibrium of such an equation is a value of x for which fx 0 because if fx 0 then xt 0 so that the value of x does not change.

A ne transformation to change our variables and create a matrix j. In a phase diagram we graph yt1 as a function of yt. For the solid liquid phase change the slope of the equilibrium curve in the p t diagram is so high that it is usually assumed that the temperature of fusion is the same at every pressure this is used to approximate the triple point by the normal melting point temperature and its corresponding vapour pressure.

Just as with the first plateau at the melting point the temperature remains constant as long as the liquid and and gas phases coexist. Point x represents the critical point and at the critical point and beyond the substance is forever in the vapor phase.

3 3 Phase Diagram For Water Vapor Clausius Clapeyron Equation