The heat death paradox, also known as thermodynamic paradox, Clausius' paradox and Kelvin’s paradox, is a ''

reductio ad absurdum In logic, (Latin for "reduction to absurdity"), also known as (Latin for "argument to absurdity") or ''apagogical arguments'', is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absu ...

'' argument that uses

thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws o ...

to show the impossibility of an infinitely old universe. It was formulated in February

1862 Events January–March * January 1 – The United Kingdom annexes Lagos Island, in modern-day Nigeria. * January 6 – French intervention in Mexico: French, Spanish and British forces arrive in Veracruz, Mexico. * January ...

Lord Kelvin William Thomson, 1st Baron Kelvin, (26 June 182417 December 1907) was a British mathematician, mathematical physicist and engineer born in Belfast. Professor of Natural Philosophy at the University of Glasgow for 53 years, he did important ...

and expanded upon by

Hermann von Helmholtz Hermann Ludwig Ferdinand von Helmholtz (31 August 1821 – 8 September 1894) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The Helmholtz Associatio ...

and

William John Macquorn Rankine William John Macquorn Rankine (; 5 July 1820 – 24 December 1872) was a Scottish mechanical engineer who also contributed to civil engineering, physics and mathematics. He was a founding contributor, with Rudolf Clausius and William Thomson ( ...

The paradox

This theoretical paradox is directed at the then-mainstream strand of belief in a classical view of a ''

sempiternal Eternity, in common parlance, means infinite time that never ends or the quality, condition, or fact of being everlasting or eternal. Classical philosophy, however, defines eternity as what is timeless or exists outside time, whereas sempit ...

'' universe, whereby its matter is postulated as everlasting and having always been recognisably the universe. Heat death paradox is borne of a paradigm resulting from fundamental ideas about the cosmos. To resolve the paradox it is necessary to change the paradigm. The paradox was based upon the rigid mechanical point of view of the

second law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unles ...

postulated by

Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Sadi Carnot's principle ...

and

, according to which heat can only be transferred from a warmer to a colder object. It notes: if the universe were eternal, as claimed classically, it should already be cold and isotropic (its objects should have the same temperature, and the distribution of matter or radiation should be even). Kelvin compared the universe to a clock that runs slower and slower, constantly dissipating energy in '' impalpable heat'', although he was unsure whether it would ''stop for ever'' (reach

thermodynamic equilibrium Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In ther ...

). According to this model, the existence of usable energy, which can be used to perform work and produce entropy, means that the clock has not stopped - since a conversion of heat in mechanical energy (which Kelvin called a ''rejuvenating universe'' scenario) is not contemplated. According to the laws of thermodynamics, any hot object transfers heat to its cooler surroundings, until everything is at the same

temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied on ...

. For two objects at the same temperature as much

heat flow Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, ...

s from one body as flows from the other, and the net effect is no change. If the universe were infinitely old, there must have been enough time for the stars to cool and warm their surroundings. Everywhere should therefore be at the same temperature and there should either be no stars, or everything should be as hot as stars. The universe should thus achieve, or asymptotically tend to, thermodynamic equilibrium, which corresponds to a state where no

thermodynamic free energy The thermodynamic free energy is a concept useful in the thermodynamics of chemical or thermal processes in engineering and science. The change in the free energy is the maximum amount of work that a thermodynamic system can perform in a process ...

is left, and therefore no further work is possible: this is the heat death of the universe, as predicted by Lord Kelvin in

1852 Events January–March * January 14 – President Louis-Napoléon Bonaparte proclaims a new constitution for the French Second Republic. * January 15 – Nine men representing various Jewish charitable organizations come t ...

. The average temperature of the cosmos should also asymptotically tend to Kelvin Zero, and it is possible that a maximum entropy state will be reached.
Laws of Thermodynamics
' Thompson and Clausius,

Oxford University press Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print book ...

, 2015

Solution

In February

used the existence of the

Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared rad ...

and the

star A star is an astronomical object comprising a luminous spheroid of plasma held together by its gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night, but their immense distances from Earth make ...

s as an empirical proof that the universe has not achieved

, as entropy production and free work are still possible, and there are temperature differences between objects.

Helmholtz Hermann Ludwig Ferdinand von Helmholtz (31 August 1821 – 8 September 1894) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The Helmholtz Association, ...

and

Rankine Rankine is a surname. Notable people with the surname include: * William Rankine (1820–1872), Scottish engineer and physicist ** Rankine body an elliptical shape of significance in fluid dynamics, named for Rankine ** Rankine scale, an absolute ...

expanded Kelvin’s work soon after. Since there are stars and colder objects, the universe is not in thermodynamic equilibrium, so it cannot be infinitely old.

Modern cosmology

The paradox does not arise in modern cosmology, which posits that the universe began in a

Big Bang The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from t ...

roughly 13.8 billion years ago – which is not long enough ago for the universe to have approached thermodynamic equilibrium.

Related paradoxes

Olbers' paradox Olbers's paradox, also known as the dark night sky paradox, is an argument in astrophysics and physical cosmology that says that the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe. In the hyp ...

is another paradox which aims to disprove an infinitely old static universe, but it only fits with a static universe scenario. Also, unlike Kelvin’s paradox, it relies on

Cosmology Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosophe ...

rather than Thermodynamics. The

Boltzmann Brain The Boltzmann brain thought experiment suggests that it might be more likely for a single brain to spontaneously form in a void (complete with a memory of having existed in our universe) rather than for the entire universe to come about in the ma ...

can also be related to Kelvin’s, as it focuses on the spontaneous generation of a brain (filled with false memories) from entropy fluctuations, in a universe which has been laying in a heat death state for an indefinite amount of time.

References

{{DEFAULTSORT:Heat death paradox Thermodynamics Physical paradoxes Physical cosmology 1862 introductions

The paradox

Solution

Modern cosmology

Related paradoxes

See also

References