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Chapter 4 Basic Milestones in the Study of Superconductivity
Therefore, the increment of free energy is
δF = δU − T δS − SδT. (4.24)
According to the first law of thermodynamics, the increment of the density of thermal
energy δQ is the sum of the work made by a sample on external bodies δR, and the
increment of its internal energy δU:
δQ = δR + δF (4.25)
as a reversible process heat increment of δQ = T δS, then
δF = −δR − SδT (4.26)
thus the entropy
( ) ∂F
S = − . (4.27)
∂T
R
In accordance with this equation,
superconducting states (4.22) can be written as:
S s − S n = H c
4π
the difference of entropy in normal and
( ∂Hc
∂T
)
. (4.28)
R
Since critical field at any temperature decreases with rising temperature:
( ) ∂Hc
< 0, (4.29)
∂T
then we can conclude (from equation (4.28)), that the superconducting state is more
ordered and therefore its entropy is lower. Besides this, since at T = 0, the derivative of
the critical field is also zero, then the entropy of the normal and superconducting state, at
this point, are equal. Any abrupt changes of the first derivatives of the thermodynamic
potential must also be absent, i.e., this transition is a transition of the order-disorder in
electron system.
Since, by definition, the specific heat C = T ( )
∂S
∂T , then the difference of specific heats
of superconducting and normal states:
[
C s − C n = T (∂Hc ) ]
2
∂ 2 H c
+ H c
4π ∂T ∂T 2 . (4.30)
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