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International Journal of Engineering Technology, Management and Applied Sciences

www.ijetmas.com September 2015, Volume 3, Special Issue, ISSN 2349-4476

162

R. Lathia, T. Agrawal, V. Parmar, K. Dobariya, A. Patel

Heat Death

(The Ultimate Fate of the Universe)

R. Lathia*, T. Agrawal, V. Parmar, K. Dobariya, A. Patel

Mechanical Engineering,

Chandubhai S. Patel Institute of Science & Technology,

CHARUSAT University,

Changa, Gujarat, India - 388421

Abstract:-

Anthropic Principle says that conditions that are observed in the universe must allow the observer to exist. At

the deep level of the existence that means the universe must have properties that make inevitable the existence of

intelligent life. But What if, the Anthropic Principle will become wrong in far further future? What If, Universe will

become a place where no life exists at all? Universe itself having Death! "Heat Death”!!!

Keywords:-

Heat Death; Anthropic Principle; Thermodynamics; Entropy

PACS Nos.:- 95.30.Tg; 05.70.-a; 05.70.Ln

1. Second law of Thermodynamics

In order to make the concept of the heat death, we must have knowledge about the second law of

thermodynamics. Second law of thermodynamics gives us the direction of flow of heat. Second law says that

the change of mechanical work into heat may be complete but heat into work must be incomplete, this means

all those processes in which work is converted into heat are unidirectional. Since, all the processes in the

universe involve conversion of small amount of work or energy into heat. It means that almost all the

processes of universe are irreversible. All this can be stated mathematically by introducing the new quantity

called Entropy.

In simple sense Entropy means the degree of randomness or degree of disorder. Mathematical

representation of change in entropy is as follows...

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

And,

ds > ∫ dQ / T (Only for Irreversible Process)

Entropy is a point function so it does not depend on the path follow by 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.

2. 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

Simplifying the concept of heat death...

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)

International Journal of Engineering Technology, Management and Applied Sciences

www.ijetmas.com September 2015, Volume 3, Special Issue, ISSN 2349-4476

163

R. Lathia, T. Agrawal, V. Parmar, K. Dobariya, A. Patel

Fig-1:- Heat Transfer through Finite Temperature Difference

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. S = SA + SB

ΔSuniverse = ΔSA + ΔSB

ΔSuniverse =

= Q

Since T1>T2, ΔSuniverse is positive and the process is irreversible and possible if T1=T2,

ΔSuniverse is Zero and the process is reversible. If T1<T2. ΔSuniverse is Negative and the process is impossible and

process will stop when Temperature of both reservoirs will become equal. In all cases the result obtained is

that isolated systems or system plus surrounding experiencing irreversible process proceed towards state of

greater disorder.

The Increase in Entropy of a system and its surrounding occur in all aging process whether in

a living organism or non-living organism, There is no doubt which condition is prior in time, youth or

maturity, structure or Erosion on condition always precedes the other; Order precedes disorder entropy always

increases during in aging processes. In short entropy is arrow of time furthermore the arrow 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 that from example we can conclude that entropy of universe increase.

ΔSuniverse > 0

Entropy may decrease locally at some region within isolated system, but it must be compensated by a

greater increase of entropy, somewhere within the system so that net effect of an irreversible process is an

entropy increase. If the entropy of an isolated system varies with some parameter 'X' (time) then there is

certain value of Xe which maximizes entropy.

And represent the equilibrium state the system is

then said to exist at the pick of the entropy hill at ds=0 when the system is in equilibrium any conceivable

change in entropy would be zero.

Fig-2:-Equilibrium State of an Isolated System

International Journal of Engineering Technology, Management and Applied Sciences

www.ijetmas.com September 2015, Volume 3, Special Issue, ISSN 2349-4476

164

R. Lathia, T. Agrawal, V. Parmar, K. Dobariya, A. Patel

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 proceed, all the available energy will be converted into

unavailable energy that situation called Heat Death.

In the case of sun and most other stars the out flow of heat can continue for many billions of years but

it is not inexhaustible. A normal star's heat is generated by nuclear processes in its interior as we shall see the

sun will eventually run out of fuel and unless overtaken by event. it will cool until it reaches the same

temperature as the surrounding space for whole universe this process will occur so that there will no more

energy or no sufficient available heat for the birth of new stars, so far further in future, There will be no stars,

No galaxy to form a new life only remain some amount of matter and black holes. Then black holes will start

to suck all the matters of the universe. At 10100years from big bang, black holes themselves will evaporate due

to Hawking radiation (Electromagnetic radiation which, according to theory, should be emitted by a black

hole. The radiation is due to the black hole capturing one of a particle-antiparticle pair created spontaneously

near to the event horizon.(Radius of a black hole)) What Remains? Only darkness. This is the Death of the

Universe.

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.

3. Effect of Time Travel on Heat Death

Most of the scientist of 21st century believes in time travel. How does time travel affect the rate of

change of entropy?

Mathematically speed required to the trip of past is minimum 3,00,000 km/sec. and for future nearby

3,00,000 km/sec but not exactly that much. In 1905, Einstein wrote about this phenomenon in his research

paper called ‘special theory of relativity’. He wrote about the strange behaviour about time, velocity and

space.

Einstein's equation for the energy required to time travel is given by.....

As v c then,

E ∞,

Because of the interaction between particle of time traveller and Higg's field (According to Pieter

Higgs, universe is a submerged in to a field known as Higg's field. It is mainly responsible for mass of the

particle, if particle having more interaction with Higg's field then it gets more mass and vice-versa. If velocity

of the particle increases, interaction increases so that the mass of the particle also increases), Time traveller

will get more and more mass, according to that we must have more energy to speed up, at speed of light

interaction will become maximum so mass of particle must become infinite, so that we must have infinite

amount of energy sources to reach up to speed of light. That’s why; huge amount of available energy will be

converted into unavailable energy. Eventually, change in entropy due to huge conversion of available energy

into unavailable energy will also increase (may be infinite). so that if time travel is possible then Heat Death

will become more nearer to us, may be several thousand years. That’s why the time travel is not advisable for

human being.

International Journal of Engineering Technology, Management and Applied Sciences

www.ijetmas.com September 2015, Volume 3, Special Issue, ISSN 2349-4476

165

R. Lathia, T. Agrawal, V. Parmar, K. Dobariya, A. Patel

'Myth' About Heat Death

Some scientists may believe that due to expansion of universe, it cools down. But it is not

true; there is no any entropy change due to expansion of the universe. We can prove that as follows...

For that we are not considering the whole universe instead of that we put an imaginary sphere around

few thousand galaxies and consider the entropy in this sphere.

As the universe expands so does the sphere whose entropy we are considering this is called the

entropy per comoving volume. We parameterize the expansion of the universe with a scale factor R. This

means that when the universe increases in size by a given factor, R increases by the same factor. The entropy

density s of a radiation field of temperature T is sT3.The entropy S in a given comoving volume V is S= s·V.

Since the commoving volume V increases as the universe expands, we have VR3. And since the temperature

of the microwave background goes down as the universe expands T1/R, we have the result that the entropy

of a given comoving volume of space SR−3R3=constant.

Thus the expansion of the universe by itself is not responsible for any entropy increase. There is no

heat exchange between different parts of the universe. The expansion is adiabatic and isentropic:

ΔSexpansion =0

4. Why Heat Death?

There are many other theories which describe the end of the universe like, Big Crunch and Big Freeze

(heat death).But why we consider only Heat death? This is the brief introduction about big crunch.

The Big Crunch is one scenario for the end of the universe. In this case, the universe contains enough

mass - it is above the critical density (If average matter density of the universe exceeds so called Critical

Density of about a 10-29gram per cubic cm (five hydrogen atoms for every cubic meter of the universe ) then a

large enough gravitational force will permeate the universe to halt and reverse the expansion. If the average

matter density is less than the critical value, the gravitational attraction will be too weak to stop the

expansion, which will continue forever.) - to stop its expansion. Once it stops expanding, it will start to

contract. Slowly at first, and then faster and faster, the universe will contract and galaxies will come closer to

each other. Eventually, everything will merge, for the universe will no longer be large enough for separate

galaxies or stars. As it continues to shrink, the universe will heat to huge temperatures, and everything will be

compacted into a black hole. Finally, at the end, the universe will be as it began - an infinitely small, infinitely

dense, and infinitely hot point. No one knows what if anything would happen after that.

An easy way to think of this is by throwing a ball; you throw a ball up into the air. Your release is like

the Big Bang, and starts the ball's acceleration. As the ball climbs skyward, it slows its ascent because the

Earth has enough gravity to slow it down and pull it back to it. This is like the mass of the universe being

enough to overcome its expansion. As the ball reaches its maximum height, it stops, which is what the

universe will do if it is over the critical density. Then, ever so slowly, the ball begins to fall back down, faster

and faster, until it reaches your hand again. This is the end of the ball's throw, and is like the end of the

universe.

In Heat Death concept, universe must have lower density than critical density. If Big Crunch theory is

right then gravity is dominating force and expansion of the universe must slow down and eventually stop. But

in 1998 Hubble Telescope proved that universe is expanding more quickly so that expanding nature of the

universe is accelerating, therefore evidence is against the Big Crunch theory so that there will be one

possibility left for the ending of the universe " Heat Death".

References:-

[01] F. Reif Fundamentals of statistical and thermal physics p120

[02] M. Zemansky, R. Dittman Heat and thermodynamics p 216

[03] B. Greene The Elegant Universe (UK: Vintage 2000) J. Cape p 234 (1999)

[04] P. Davies Last Three Minutes Ch 2 (1993)

[05] W. Drees Beyond the Big Bang: Quantum Cosmologies and God p 272

[06] S. Sisti The Big Bang and relative Immortality: Seminal Essays on the creation of the Universe p 03

[07] P. K. Nag Engineering thermodynamics (INDIA: TATA McGRAW-HILL) S.Mukerjee p 167(2010)

[08] S. Weinberg The First Three Minutes (Fontana Paperbacks)

International Journal of Engineering Technology, Management and Applied Sciences

www.ijetmas.com September 2015, Volume 3, Special Issue, ISSN 2349-4476

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R. Lathia, T. Agrawal, V. Parmar, K. Dobariya, A. Patel

[09] F. C. Adams, G. Laughlin A Dying Universe-The Long Term Fate and Evolution of Astrophysical Object (1996)

[10] G. Giorbran A Bleak and Meaningless Universe...Not! (2007)

[11] R.E. Ulanowicz Increasing Entropy: Heat Death or Perpetual Harmonies? Vol. No. 2 (2009)

[12] P. Harremoes, F. Topsoe Maximum Entropy Fundamentals (2001)

[13] S. Solomon, N. Golo How Do Life, Economy and Other Complex Systems Escape the Heat Death?(2014)

[14] C. H. Lineweaver, C. A. Egan Life, gravity and the second law of thermodynamics (2008)

[15] K. Martinás, A. Grandpierre Thermodynamics Measure for nonequilibrium processes (2007)

[16] C. H. Lineweaver Cosmological and Biological Reproducibility:Limits on the Maximum Entropy Production

Principle

[17] G. Giorbran The Superstructure of an Infinite Universe (1994)

[18] G. Giobran At the Shore of an Infinite Ocean (1996);

[19] G. Giobran Exploring a Many Worlds Universe (1997)