Processing & Properties of Floor and Wall Tiles.pptx
Theme 5.pptx
1. Theme 5: Entropy and
Second Law of
Thermodynamics
STUDENT: MORENO SAAVEDRA JOSE SAUL
2. Reversible and Irreversible Process
The first law of thermodynamics leads to a balance equation of the energy that must be met for
all physical processes that occur in the reality:
3. In particular, if we consider an isolated system (a system that cannot exchange energy with the
outside), the temporal variation of the total energy of the system will be null.
and therefore the energy balance equation , established by the first law of thermodynamics,
imposes that any variation of internal energy has to compensate with an equal and opposite
variation of kinetic energy.
4. What the first law of thermodynamics does not say is whether this exchange of energies
(kinetic and internal) in an isolated system can produce indistinctly in any sense
Or
5. Example:
• a rigid (non-deformable) wheel that
rotates with angular velocity ω
• a brake that can be applied on
the wheel at a certain instant
6. Let us now consider the following two processes:
1. At a certain instant the brake acts, the speed of rotation of the wheel, ω, decreases and
therefore its kinetic energy decreases.
2. Keeping the brake released, at a certain instant the wheel increases spontaneously its
speed of rotation ω and therefore increases its energy kinetics
dK < 0 ; dU > 0
dU < 0 ; dK > 0
8. Reversible process: A thermodynamic process A → B is reversible if it is
possible to return from the final thermodynamic state B to the state
initial thermodynamic A, by the same path.
Irreversible process: A thermodynamic process A → B is irreversible if
it is not possible to return from the final thermodynamic state B to the state
initial thermodynamic A, by the same path (although it can be returned to the
same by a different way.
10. The second law of thermodynamics states the following two
postulates:
1. There is a state function called absolute temperature θ(x,t) which is
intensive and strictly positive ( θ > 0 ).
2. There is a state function called entropy S with the following
characteristics:
a) It is an extensive variable (the content of entropy in the whole is the
sum of the content in the parts). This implies that there is an entropy
specific (entropy per unit mass) s such that:
11. b) The following inequality holds:
where:
if sign = 0 𝑟𝑒𝑣𝑒𝑟𝑠𝑖𝑏𝑙𝑒 𝑝𝑟𝑜𝑐𝑒𝑠𝑠
if sign > 0 𝑖𝑟𝑟𝑒𝑣𝑒𝑟𝑠𝑖𝑏𝑙𝑒 𝑝𝑟𝑜𝑐𝑒𝑠𝑠
if sign 0 < 𝑛𝑜𝑡 𝑓𝑎𝑐𝑡𝑖𝑏𝑙𝑒 𝑝𝑟𝑜𝑐𝑒𝑠s
:
12. Physical interpretation of the second law
of thermodynamics
The quantity of heat in the system is characterized by:
a) a source term (or heat generation per unit mass and of time) r(x,t) , defined inside the
material volume and
b) the non-convective flow (heat flow by conduction) through the contour of the material
surface, defined by a flux vector non-convective per unit area q(x,t) .
With these terms we can calculate the amount of heat that enters per unit of time in a material
volume Vt , which instantly occupies the volume of the space Vt ≡V of exterior normal n , as:
13. Let us now consider a new quantity defined as heat per unit of absolute temperature in the
system. If θ(x,t) is the absolute temperature, the amount of said magnitude will be
characterized by:
a) a source term r/ θ corresponding to the generation of heat by unit of absolute
temperature, per unit of mass and unit of time.
b) a vector q/ θ of non-convective flow of heat per unit of temperature absolute.
:
14. The new terms source and vector of non-convective flow allow calculating the amount of heat
per unit of absolute temperature entering the material volume per unit time as:
This circumstance allows us to interpret the second principle establishing that “The entropy
generation, per unit time, in a continuous medium is always greater than or equal to the
amount of heat per unit temperature entering the system per unit time”
:
15. Let us now consider the decomposition of the total entropy of the system S into
two distinct components:
a) 𝑆𝑖 : entropy generated (produced) internally by the continuous medium.
b) 𝑆𝑒 : entropy generated by the interaction of the continuous medium with its exterior.
16. If it is now established that the time variation of the entropy generated by interaction with the
outside coincides with that of the magnitude heat per unit of absolute temperature, can be
written:
17. In a perfectly isolated system (strictly speaking, only the totality of the universe is) there is no
interaction with the outside and the change of entropy by interaction with the outside is zero
In this case, the second principle states that the total entropy of a perfectly isolated always
increases.
18. Restatement of the second law of
thermodynamics.
We can reformulate the second principle in the following terms:
1. There is a state function called absolute temperature such that is always strictly positive:
2. There is a state function called entropy which is a variable extensive and can therefore be
defined as a function of an entropy specific (or entropy per unit mass) s(x,t) as:
19. 3. Entropy can be internally generated, or produced by interaction with the outside, Both
components of entropy are extensive variables and their content in a material volume V
can be defined according to their respective specific values:
and using Reynolds' lemma:
20. The external entropy variation (generated by interaction with the outside) It is associated with
the variation of the magnitude of heat per unit of temperature absolute, and is defined as:
The entropy of internal generation never decreases. Depending on the variation of its content
during a thermodynamic process are defined the following situations:
