Order of phase transitions I got to read things  like 

In case of a first order phase transition, the volume and temperature change in a discontinuous manner. However for phase transitions of higher order the change in volume and temperature can be continuous. 

I could not exactly understand the statement and thats why I thought what exactly it means by the order of a phase transition.
May I know what exactly it means by the order of phase transition? 
 A: In the graphic included in the related Wikipedia article, depicted is a type of space where the axes are thermodynamic variables.  You can similarly just think of any two dimensional plot with a line drawn on it.  The line can be understood to represent a function.  Normally if you want to find the slope of a function, you take the first derivative of that function.  If the first derivative of the function has a discontinuity (e.g. a point were the function is no longer well defined), and the variable in question is a thermodynamic variable, then by definition the phase transition is a first order phase transition (because the discontinuity occurs in the in the first derivative of the function).  
Essentially, the scheme is using an understanding of the properties of derivatives of math functions in order classify the types of phase transitions. Without a proper understanding of the related mathematical concept, its understandable that this classification isn't immediately obvious. I hope this helps. 
A: Broadly speaking Hal is right. Let me try to make it a bit more transparent if you don't mind. The 1st derivative of the Gibbs free-energy of the system w.r.t T, at constant P, is the entropy of the system, while the derivative w.r.t P, at constant T, is the volume. If these quantities are discontinuous at the CP (critical point,) the phase transition is said to be first order, because of the singularity of the 1st derivative. On the other hand, the 2nd derivative w.r.t T, at constant P, relates to the specific heat of the system. If the specific heat is singular at the CP then the phase transition is said to be second order. Therefore, the terms 1st and 2nd order phase transition are general, and distinguish one type from the other, as the physics behind these two can relate to very different properties of condensed matter or other fields of physics. For example, at an elastic 1st order phase transition the volume and entropy of the crystal undergo abrupt change at CP. If the transition is 2nd order, the specific heat of the crystal grows singularly, and at the same time the speed of the vibrational mode leading the transition tends to zero (mode softening!)
