Entropy
Entropy is a quantity in physics that measures how much of a system's energy is not available to do work. It can also be shown to be a measure of the system's disorder.[1] Entropy is at the heart of the second law of thermodynamics, which says that the total entropy of a closed system never decreases.[2][3]
Measuring entropy
When heat is added to or removed from a system in a reversible way, the change in entropy is the heat transferred divided by the absolute temperature (in kelvins) at which it is transferred. Entropy is measured in joules per kelvin (J/K). Adding heat increases entropy, and removing it decreases entropy.[1][4]
Entropy is a property of the state of a system. The change in entropy between two states is the same however the change happens, so it can be worked out by imagining any reversible process that links the same starting and finishing states.[5][6][3]
The second law of thermodynamics
The first law of thermodynamics is the conservation of energy: heat added to a system goes into raising its internal energy and doing work.[3] The second law can be stated in terms of entropy. In a closed system, entropy increases during irreversible processes and stays the same during reversible ones.[7] In the real world almost every process is irreversible to some extent, because of friction, turbulence and other effects, so the entropy of real closed systems always increases.[7] In the words of one physics textbook, "Entropy is not conserved but increases in all real processes."[2]
An example of an irreversible process is a gas expanding to fill an empty container. Once the gas has spread out, its molecules will never all return to one half of the container by themselves.[4]
The second law can also be stated without mentioning entropy: no process is possible whose only result is to move heat from a colder place to a hotter one.[8] It also sets a limit on how efficient a heat engine can be. No real engine can be more efficient than an ideal engine, called a Carnot engine, working between the same two temperatures.[9][10]
Entropy and probability
Entropy is closely linked to probability: the more likely a state is, the greater its entropy.[11] Imagine tossing 100 coins. There is only one way for them all to land heads, but about 1029 ways to get 50 heads and 50 tails. Even tossing them once a second, getting all heads again would take an unimaginably long time.[12] In the same way, there are vastly more ways for gas molecules to be spread evenly through a room than gathered in one corner, so a gas never collects in one corner by itself.[11][13]
In 1877 the Austrian physicist Ludwig Boltzmann found a relationship between the entropy of a gas and the number of ways its molecules can be arranged. His formula, S = k ln W, is engraved on his tombstone.[14][14][11]
Everyday examples
A stretched rubber band pulls back partly because its polymer molecules tend to return to a more disordered state with higher entropy.[15] A kilogram of melted ice at 0 °C cannot refreeze by itself, because that would need a decrease in entropy.[16]
The future of the universe
As entropy increases, less and less of the energy in the universe is available to do work. The final state, in which no energy is available, is sometimes called the "heat death of the universe".[17]
See also
References
- ↑ 1.0 1.1 Urone, Paul Peter; Hinrichs, Roger (2017) [2012]. College Physics. Houston: OpenStax. p. 585. ISBN 978-1-938168-00-0. Retrieved 2026-10-23.
- ↑ 2.0 2.1 Urone, Paul Peter; Hinrichs, Roger (2017) [2012]. College Physics. Houston: OpenStax. p. 587. ISBN 978-1-938168-00-0. Retrieved 2026-10-23.
- ↑ 3.0 3.1 3.2 Boeker, Egbert; van Grondelle, Rienk (2011). Environmental Physics: Sustainable Energy and Climate Change (3rd ed.). Chichester: John Wiley & Sons. section 4.2.1: First and Second Laws. ISBN 978-0-470-66676-0. Retrieved 2026-10-23.
- ↑ 4.0 4.1 Halliday, David; Resnick, Robert; Walker, Jearl (2021). Fundamentals of Physics. Adapted by Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius O. Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons and Dipesh Bhattarai (1st Australian & New Zealand ed.). Milton, Qld: John Wiley & Sons Australia. p. 433. ISBN 9780730382898.
{{cite book}}:|access-date=requires|url=(help) - ↑ Urone, Paul Peter; Hinrichs, Roger (2017) [2012]. College Physics. Houston: OpenStax. pp. 585–586. ISBN 978-1-938168-00-0. Retrieved 2026-10-23.
- ↑ Halliday, David; Resnick, Robert; Walker, Jearl (2021). Fundamentals of Physics. Adapted by Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius O. Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons and Dipesh Bhattarai (1st Australian & New Zealand ed.). Milton, Qld: John Wiley & Sons Australia. p. 435. ISBN 9780730382898.
{{cite book}}:|access-date=requires|url=(help) - ↑ 7.0 7.1 Halliday, David; Resnick, Robert; Walker, Jearl (2021). Fundamentals of Physics. Adapted by Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius O. Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons and Dipesh Bhattarai (1st Australian & New Zealand ed.). Milton, Qld: John Wiley & Sons Australia. p. 436. ISBN 9780730382898.
{{cite book}}:|access-date=requires|url=(help) - ↑ Halliday, David; Resnick, Robert; Walker, Jearl (2021). Fundamentals of Physics. Adapted by Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius O. Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons and Dipesh Bhattarai (1st Australian & New Zealand ed.). Milton, Qld: John Wiley & Sons Australia. p. 448. ISBN 9780730382898.
{{cite book}}:|access-date=requires|url=(help) - ↑ Halliday, David; Resnick, Robert; Walker, Jearl (2021). Fundamentals of Physics. Adapted by Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius O. Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons and Dipesh Bhattarai (1st Australian & New Zealand ed.). Milton, Qld: John Wiley & Sons Australia. pp. 450–451. ISBN 9780730382898.
{{cite book}}:|access-date=requires|url=(help) - ↑ Boeker, Egbert; van Grondelle, Rienk (2011). Environmental Physics: Sustainable Energy and Climate Change (3rd ed.). Chichester: John Wiley & Sons. section 4.2.2: Heat and Work; Carnot Efficiency. ISBN 978-0-470-66676-0. Retrieved 2026-10-23.
- ↑ 11.0 11.1 11.2 Urone, Paul Peter; Hinrichs, Roger (2017) [2012]. College Physics. Houston: OpenStax. p. 595. ISBN 978-1-938168-00-0. Retrieved 2026-10-23.
- ↑ Urone, Paul Peter; Hinrichs, Roger (2017) [2012]. College Physics. Houston: OpenStax. p. 594. ISBN 978-1-938168-00-0. Retrieved 2026-10-23.
- ↑ Halliday, David; Resnick, Robert; Walker, Jearl (2021). Fundamentals of Physics. Adapted by Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius O. Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons and Dipesh Bhattarai (1st Australian & New Zealand ed.). Milton, Qld: John Wiley & Sons Australia. p. 454. ISBN 9780730382898.
{{cite book}}:|access-date=requires|url=(help) - ↑ 14.0 14.1 Halliday, David; Resnick, Robert; Walker, Jearl (2021). Fundamentals of Physics. Adapted by Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius O. Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons and Dipesh Bhattarai (1st Australian & New Zealand ed.). Milton, Qld: John Wiley & Sons Australia. p. 453. ISBN 9780730382898.
{{cite book}}:|access-date=requires|url=(help) - ↑ Halliday, David; Resnick, Robert; Walker, Jearl (2021). Fundamentals of Physics. Adapted by Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius O. Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons and Dipesh Bhattarai (1st Australian & New Zealand ed.). Milton, Qld: John Wiley & Sons Australia. p. 437. ISBN 9780730382898.
{{cite book}}:|access-date=requires|url=(help) - ↑ Urone, Paul Peter; Hinrichs, Roger (2017) [2012]. College Physics. Houston: OpenStax. p. 596. ISBN 978-1-938168-00-0. Retrieved 2026-10-23.
- ↑ Urone, Paul Peter; Hinrichs, Roger (2017) [2012]. College Physics. Houston: OpenStax. p. 589. ISBN 978-1-938168-00-0. Retrieved 2026-10-23.