Extensive and Intensive
Parameters/Properties
MSE 308
Thermodynamics of
Materials
‰ Consider a System:
9 At Equilibrium
9 No gradients within the system
9 Described by a parameter say yi.
y1 + y2 = y
y1 = y2 = y
Extensive
Parameter
Or Variable
Intensive
Parameter
Or Variable
Knowlton
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MSE 308
Thermodynamics of
Materials
Other Parameters/Properties/Variables
‰ Classification of Variables/Properties/Parameters:
9 Extensive:
o Additive
o State variables (only sometimes)
9 Intensive:
o Not additive
o Field Variables
o Point Variables (i.e., same at each point in a system at equilibrium)
9 Normalized Extensive are Intensive:
o Ratio of Extensive:Intensive (Extensive/Intensive )
o Densities
o Not additive
9 Process:
o Path dependent – dependent on past history
o Inexact differentials
9 Conjugate Variables: (see next page)
Knowlton
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1
Extensive and Intensive
Parameters/Properties/Variables
MSE 308
Thermodynamics of
Materials
‰ Intensive Parameters:
9P
9T
9µ
9 ξ (electric field)
9 Any field variable
9 Ratio of Extensive/Extensive
‰ Extensive Parameters:
9Q
o indeed is an extensive parameter
o Process variable (not a quantity
but transfers from one state to the
next)
9 W (work)
o indeed is an extensive parameter
o Process variable (not a quantity
but transfers from one state to the
next)
9
9
9
9
9
9
o N/M or N/V or M/V
o These are known as specific
properties
U (and other free energies)
N
V
M (mass)
C (heat capacity)
n moles
Knowlton
3
MSE 308
Thermodynamics of
Materials
Conjugate Variables
∑ δ W = ∑ YdX
Table 2.1: Types of thermodynamic work in differential form
Thermodynamic
Work
Knowlton
Work
Differential
(dW)
Intensive or
Field Variable
Extensive or State
Variable
thermal
T•dS
T = temperature
S = entropy
hydrostatic
P•dV
chemical
µ•dN
P = pressure
µ = chemical
potential
V = volume
N = number of
particles
strain –
mechanical
electrical
σ •dε
σ = stress
ε = strain
E•dP o
E = electric field
P o = polarization
magnetic
H•dM g
H = magnetic field
M g = magnetization
time
dependent
P w•dt
P w = power
t = time
Momentum
transfer
ma•dr
Mass
acceleration
gravitational
mg•dr
mg = mass &
gravitational
acceleration
&
and: Voltage ⋅ dq
r = distance
r = distance
Note: The intensive and extensive variable
pairs are known as conjugate variables. For
example, T and S are conjugate variables.
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MSE 308
Thermodynamics of
Materials
Equilibrium
Some Thermodynamic Potential, E
‰ Types of Equilibrium States:
9 Stable
9 Metastable
9 Unstable 10
8
Transition State
6
Unstable
Equilibrium
State
4
2
0
Metastable
Equilibrium
State
-2
-4
-6
Stable Equilibrium State
-8
-2
Knowlton
-1
0
1
Reaction Coordinates, ξ
2
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MSE 308
Thermodynamics of
Materials
Comments on Energy, Entropy, Heat & Work
‰ Energy and Entropy:
9 "It would be preferable, but for the need for economy of words, to speak
always of 'energy function' and 'entropy function' rather than of energy
and entropy.
9 They are not material entities, but are mathematical functions having
certain properties.
‰ Versus Heat and Work:
9 It is always permissible to speak of the energy and entropy content of a
body relative to some other State.
9 In the same light, it is not permissible to speak of a body's heat or work
content.
9 Heat and work are modes of transfer of energy between one body and
another. Hence, they are path dependent and process variables.
Knowlton
» Bridgman, The Nature of Thermodynamics (Harvard, 1941)
» Denbigh, The Principles of Chemical Equilibrium (Cambridge University Press,
1981)
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