Question

Discontinuity in specific heat during phase transition

Answer 1

Classification of phase transitions
Discontinuous phase transitions are characterised by a discontinuous change in entropy at a
fixed temperature. The change in entropy corresponds to latent heat L = T ∆S. Examples
are solid–liquid and liquid–gas transitions at temperatures below the critical temperature.
Continuous phase transitions involve a continuous change in entropy, which means there
is no latent heat. Examples are liquid–gas transitions at temperatures above the critical
temperature, metal–superconductor transitions and many magnetic ordering transitions.
Ehrenfest’s classification scheme: the order of a transition is the order of the lowest
differential of G which shows a discontinuity.
First order transitions have discontinuities in the first derivatives of G:
(
∂G
∂T )
p
= −S, (
∂G
∂p )
T
= V.
First order transitions are therefore discontinuous.
Second order transitions have discontinuities in the second derivatives of G:
(
∂
2G
∂T2
)
p
= −
cp
T
,
(
∂
2G
∂p2
)
T
= −V κT ,
(
∂
2G
∂T ∂p)
= V βp
Second order transitions are examples of continuous transitions.
Phase transitions often involve the development of some type of order with an associated
symmetry breaking. The broken symmetry is described by an order parameter which
usually increases on moving deeper into the ordered phase, and which measures the degree of
order as the phase transition proceeds. The order parameter is a physical observable, usually
related to a first derivative of G. Examples of order parameters are magnetisation M for a
ferromagnet, electrical polarisation P for a ferroelectric, and the degree of alignment of the