Heat death of the Universe/the big freeze/ the end of the universe quantum mechanically and statistical mechanically.

2. HEAT DEATH OF
THE UNIVERSE
Presented by:
ZERMEEN FATIMA
QURT UL AIN

3. THE FATE OF THE UNIVERSE
The heat death of the universe, also known as the Big Chill
or Big Freeze, is a supposition on the ultimate fate of
the universe, which suggests that the universe would evolve
to a state of no thermodynamic free energy and would
therefore be unable to sustain processes that increase
entropy.

4. THE ANTHROPIC PRINCIPLE
•This principle states that the conditions that exist in universe must
allow an observer to exist.
•If ANTHROPIC PRINCIPLE becomes wrong in the future then the
Universe itself will die.
•Heat death would be the reason which is our topic to discuss today.
•For the understanding of heat death of the universe, one must know
about the Entropy and 2nd Law of Thermodynamics.

5. 2nd LAW OF THERMODYNAMICS AND ENTROPY
•A thermodynamic quantity
representing the unavailability of a
system's thermal energy for
conversion into mechanical work,
often interpreted as the degree of
disorder or randomness in the
system.
•The Second Law of
Thermodynamics says that
processes that involve the transfer
or conversion of heat energy are
irreversible. The Second Law also
states that there is a natural
tendency of any isolated system to
degenerate into a more disordered
state i.e maximum entropy.

6. •Entropy is a point function that depends only on the current equilibrium state of the
system.
•If end state of reversible and irreversible process is same then entropy change will be
same.
•If change in entropy is more, available work decreases and possibility of conversion of
heat into work decreases.
ds = ∫ dQ / T (Only for Reversible Process)
Here
ds = change in entropy
dQ = heat supplied or given out by a body (Available work for
system) - (work done by system) T = temperature of body. &:
ds > ∫ dQ / T (Only for Irreversible Process)

7. How Exactly will The Universe Fall Apart? Heat Death.
How?????
• Heat Death is the phenomenon in which all processes will eventually stop, no
further work can proceed due to irreversible nature of entropy and time.
• For universe, heat death is defined as...
"A Suggested ultimate fate of universe in which the universe has diminished
to a state of no thermodynamic free energy and therefore can no longer
sustain processes that consume energy."
- Rudolf Clausius

8. THERMODYNAMICALLY:
•According to second law of thermodynamics heat always flows from hot body
to cold body. For that we can derive expression of change in entropy. Let Q be
the rate of heat transfer from reservoir A at T1 to reservoir B at T2, (T1>T2)

9. • For Reservoir A, ΔSA = - Q / T1. It is negative because heat Q flows out of the reservoir.
• For Reservoir B, ΔSB = + Q / T2. It is Positive because heat flows into the reservoir.
• The rod connecting the reservoirs surfaces no entropy change because once in the steady
state, its coordinates do not change. Therefore, for the isolated system comprising the
reservoirs and the rod, and since entropy is an additive property.
• Since T1>T2, ΔSuniverse is positive and the process is irreversible.
• If T1<T2. ΔSuniverse is Negative and the process is impossible.
• Process will stop when Temperature of both reservoirs will become equal.

10. • In all cases the result obtained is that isolated system plus surrounding experiencing
irreversible process proceed towards state of greater disorder.
•Entropy is arrow of time that has only one direction it points forward into future.
Entropy always increases with increasing time and at equilibrium state entropy will
become maximum. System and surrounding together form universe.
Since, universe is an isolated system so we can conclude that entropy of universe increase.
•ΔSuniverse > 0
• As shown in graph if universe reaches at the state of
maximum entropy or the equilibrium state universe
will cool down, no further work can be proceeded, all
the available energy will be converted into
unavailable energy that situation called Heat Death.

11. • Since Big Bang average temperature of universe constantly decreases. 10-43sec after the big bang
temperature of universe became 1032K but now average temperature of the universe is 2.73K. It
means universe cools down towards the absolute zero temperature. Mathematical expression for
that is given by...
• Change in entropy of universe
ΔSuniverse = ΔQ / T
Here, T = final temperature of the universe T must going towards absolute Zero.
.·. T 0 so that ΔS ∞
• This is the case of maximum entropy. In this highly disordered state, no heat or energy interaction can
proceed and all the process in the universe will eventually stop. negative temperature in Kelvin scale
is not possible (The third law of thermodynamics) so that no further temperature reduction is possible
and universe remain in that condition forever, that's why Heat Death is also known as Big Freeze or
Cold Death.

12. THE STATISTICAL MECHANICS APPROACH
Let us start by considering:
• n number of particles where n is a very great number.
• Their Microstates are Position & Momenta.
• Each position is determined by three coordinates q; (e.g. the rectangular coordinates x, y
and z) and each momentum vector by its three components pi (e.g. mvx, mvy and mvz
where m is the mass and v the velocity vector)
• The microstate is therefore determined by 3n coordinates of position qi(i = 1 to 3n) and
3n components of momentum pi. Considering these momentum components also as
coordinates, one can represent the microstate in a generalized space of 6n dimensions
called PHASE SPACE (containing all possible values
of position and momentum variables)

13. • In thermodynamics the macro-state of a single system was fixed by two quantities, its internal
energy U and its volume V. In statistical mechanics each micro-state has same fixed internal
energy U and volume V, the macrosystem is represented by the ensemble or assembly of all
these micro-states taken together. Since each micro-system is a point in state space, the macro-
system is a cluster of such points occupying a generalized volume, in phase space, called the Phase
Extension ∑.
• As we know:
P(s): Probability of a system in state s and P(s)= 1/g
g: Accessible state
X: is any parameter. Then
<x> =
∑X(s)
𝑔

14. • Lorentz considers such a system of energy U and volume V and then keeps V constant letting the
energy vary between the values U +dU. So he defines the Probability of microstate by:
g=
𝒅∑
𝒅𝑼
Where: 𝒅∑ is the total phase extension corresponding to the volume V & the energy interval dU
between U+dU.
• In Statistical Mechanics the 'Equiprobability Principle’ states that:
“In a state of thermal equilibrium, all the accessible microstates of the system are equally
probable.”
• hence according to the above formula the g dU becomes proportional to the number of microstates
in 𝑑∑

15. • Now coming to the definition of Entropy in Statistical view which involves Boltzman Constant.
S=k ln(g)
• As we are talking about the universe itself which is a compound system x made up of y single
systems then g= g1, g2, ….. Gy. Then:
ln(g) = ∑ 𝒙=𝟏
𝒚
ln(gx) & S = ∑ 𝒙=𝟏
𝒚
𝑺x
• Consider mixing equal volumes of water of 0° and l00°C to water of 50°C), then the transition
from a lower to a higher state probability g occurs enormously much more frequently than the
transition from a higher to a lower if this takes place spontaneously. In other words, a thermally
insulated system has the capability of having its probability of state increasing, but extremely
rarely decreasing. So, for the overwhelming majority of cases:
𝒅𝒈
𝒅𝒕
≥ 𝟎 𝒇𝒐𝒓 𝒅𝑸 = 𝟎
*Equality sign indicates when g reaches maximum value

16. • Thus from the above two equations:
• This is the form of 2nd Law of
Thermodynamics which means that for
adiabatic processes the entropy of a system
increases with time if the process is
irreversible. Isolated systems
spontaneously evolve
towards thermodynamic equilibrium,
the state with maximum entropy.
𝒅𝑺
𝒅𝒕
≥ 𝟎 𝒇𝒐𝒓 𝒅𝑸 = 𝟎

17. HELMHOLTZ FREE ENERGY AND HEAT DEATH
• Free energy, in thermodynamics, is energy-like property or state function of a
system in thermodynamic equilibrium. It has the dimensions of energy & its value
is determined by the state of the system and not by its history. Free energy is used
to determine how systems change and how much work they can produce. It is
expressed as the Helmholtz free energy F, sometimes called the work function.

18. F= U - Ʈδ
• For equilibrium F is minimum and entropy is maximum according to this equation.
If there is no free energy left to do the work obviously the system (Universe) will
be in a state of maximum entropy and thus there will be no more heat exchange
that could do some work and this way the system will have the same temperature
everywhere. When temperature and volume are constant then F will always be
minimum.
dF = dU- Ʈ dδ eq 1
Where: Ʈ =
𝟃𝑼
𝟃δ
so Ʈ𝟃δ = 𝟃U
So eq1 becomes: dF= Ʈ dδ - Ʈ dδ
dF = 0
*Which means free energy would be minimum. And no work can be further
done.

19. Conclusion:
• The Universe continues to expand, eventually to a state of zero
thermodynamic free energy — no longer able to sustain motion or life.
• In one hundred trillion years or so, the Universe will reach a state of
maximum entropy at a temperature very close to absolute zero (-273.15
degrees Celsius or -459.67 degrees Fahrenheit) — the temperature at which
atoms stop moving — making the Universe too cold to support life.
• All existing stars would eventually burn out, leaving black holes, which would
too evaporate as the Universe gets colder. Thus leaving a Universe of cold,
dead planets.