The thermodynamic **properties of materials** are intensive thermodynamic parameters which are specific to a given material. Each is directly related to a second order differential of a thermodynamic potential. Examples for a simple 1-component system are:

**Compressibility** (or its inverse, the **bulk modulus**)
Isothermal compressibility
β
T
=
−
1
V
(
∂
V
∂
P
)
T
=
−
1
V
∂
2
G
∂
P
2
Adiabatic compressibility
β
S
=
−
1
V
(
∂
V
∂
P
)
S
=
−
1
V
∂
2
H
∂
P
2
**Specific heat** (Note - the extensive analog is the **heat capacity**)
Specific heat at constant pressure
c
P
=
T
N
(
∂
S
∂
T
)
P
=
−
T
N
∂
2
G
∂
T
2
Specific heat at constant volume
c
V
=
T
N
(
∂
S
∂
T
)
V
=
−
T
N
∂
2
A
∂
T
2
**Coefficient of thermal expansion**
where *P* is pressure, *V* is volume, *T* is temperature, *S* is entropy, and *N* is the number of particles.

For a single component system, only three second derivatives are needed in order to derive all others, and so only three material properties are needed to derive all others. For a single component system, the "standard" three parameters are the isothermal compressibility
β
T
, the specific heat at constant pressure
c
P
, and the coefficient of thermal expansion
α
.

For example, the following equations are true:

c
P
=
c
V
+
T
V
α
2
N
β
T
β
T
=
β
S
+
T
V
α
2
N
c
P
The three "standard" properties are in fact the three possible second derivatives of the Gibbs free energy with respect to temperature and pressure.