The document discusses several thermodynamic concepts and relationships including: 1) The Helmholtz and Gibbs free energy functions, which relate the work done, internal energy, temperature, and entropy or enthalpy of a system. 2) Gibbs phase equilibrium condition, which states that for a system at constant temperature and pressure, the equilibrium state is the one that minimizes the Gibbs free energy. 3) The Clausius-Clapeyron equation, which describes the relationship between pressure and temperature during a phase change at constant temperature.

1. General thermodynamic
properties and its relation
S.Gunabalan
Associate Professor
Mechanical Engineering Department
Bharathiyar College of Engineering & Technology
Karaikal - 609 609.
e-Mail : gunabalans@yahoo.com
Part - 2

2. HELM HOLTZ AND GIBBS FUNCTIONS
The work done in a non-flow reversible system
(per unit mass) is given by
W = Q – (u0 – u1)
= T.ds – (u0 – u1)
= T.(s0-s1) – (u0 – u1)
= (u1 – Ts1) – (u0 – Ts0)
The term (u – Ts) is known as Helmholtz
function

3. This gives maximum possible output
– when the heat Q is transferred at constant temperature
This can be achieved through a very large source.
work against atmosphere = p0 (v0 – v1)
then the maximum work available,
Wmax = W – work against atmosphere
= W – p0 (v0 – v1)
= (u1 – Ts1) – (u0 – Ts0) – p0 (v0 – v1)
= (u1 + p0v1 – Ts1) – (u0 + p0v0 – Ts0)
= (h1 – Ts1) – (h0 – Ts0)
Wmax = g1 – g0
where g = h – T.s is known as Gibb’s function or free
energy function

4. Gibbs Phase Equilibrium Condition
• A system is said to be in thermodynamic
equilibrium if, when it is isolated from its
surroundings, there would be no
macroscopically observable changes.
• An important requirement for equilibrium is
that the temperature be uniform throughout
the system or each part of the system in
thermal contact.

5. Consider the compressible system of fixed mass for
which temperature and pressure are uniform with
position throughout.
In the absence of overall system motion and
ignoring the influence of gravity,
the energy balance in differential form
= − W
W = pdV
= −
= +

7. − = +
− − = ------------ (eq.1)
Entropy is produced ( )in all actual processes and
conserved only in the absence of irreversibilities.
Hence, Eq.1 provides a constraint on the direction of
processes. The only processes allowed are those for
which >= 0. Thus
− − ≥ 0
This equation used to study equilibrium under various
conditions.

8. a process taking place in an insulated, constant-
volume vessel, where dU = 0 and dV = 0, must
be such that
≥ 0
this equation suggests that changes of state of a
closed system at constant internal
energy and volume can occur only in the
direction of increasing entropy.
The expression also implies that entropy
approaches a maximum as a state of
equilibrium is approached.

9. In a study of chemical and phase equilibria is
one in which temperature and pressure are fixed

10. Gibbs Phase Equilibrium Condition
Any process taking place at
a specified
temperature and pressure
(dT = 0 and dp = 0) must
be such that
The equilibrium state is the one having the minimum value of the Gibbs function

11. Values of two
independent
intensive properties
are sufficient to fix
the intensive state
of a simple
compressible system
of specified mass
and composition
Thermodynamic Relations

14. Similar to

16. Clapeyran Equation
During a phase change at fixed temperature,
the pressure is independent of specific
volume and is determined by temperature
alone. Thus,

17. Clapeyran Equation

19. (1) f is negligible in comparison to g,
(2) the pressure is low enough that g can be
evaluated from the ideal gas equation of state as
g = RT/p

20. Reference
• Moran, M. J. 2011. Fundamentals of engineering thermodynamics. Wiley,
[Hoboken, N.J.?].