# Entropy balance

The entropy balance is a balance equation of thermodynamics . It considers the entropy added or removed via the system boundary of a thermodynamic system and the entropy produced within the system.

## Balance equation

In thermodynamics, entropy is understood as a state variable and can therefore be balanced , like mass and energy in a system, for example. If you insert the entropy into the general balance equation , you get the term

${\ displaystyle dS = \ sum _ {i} dS_ {i} ^ {SG} + dS ^ {Q}}$.

It is

${\ displaystyle S}$ the entropy
${\ displaystyle dS ^ {SG}}$ an entropy flow over the system boundary
${\ displaystyle \ textstyle \ sum _ {i} dS_ {i} ^ {SG}}$ the sum of all entropy flows over the system boundary
${\ displaystyle dS ^ {Q}}$ the change in entropy within the system.

Entropy can enter or exit the balance space in the form of heat or together with matter added or removed from the system. For the sum of all entropy flows across the system boundary, the following applies:

${\ displaystyle \ sum _ {i} dS_ {i} ^ {SG} = dS_ {Q} + dS_ {M}}$.

It is

${\ displaystyle dS_ {Q}}$ the change in entropy due to heat
${\ displaystyle dS_ {M}}$ the change in entropy due to matter transport.

If you insert this term into the top equation and specify the source term by replacing it with , you get the entropy balance in the form ${\ displaystyle dS ^ {Q}}$${\ displaystyle S_ {irr}}$

${\ displaystyle dS = dS_ {Q} + dS_ {M} + dS_ {irr}}$.

This equation reads for continuous processes

${\ displaystyle {\ frac {dS} {d \ tau}} = {\ dot {S}} _ {Q} + {\ dot {S}} _ {M} + {\ dot {S}} _ {irr }}$.

There is time. ${\ displaystyle \ tau}$

According to the sign convention, entropy generated or added is positive, while entropy removed is negative. Entropy can either be increased or decreased via the energy form heat or via the transport of matter. and consequently can be positive or negative. The source term, on the other hand, denotes the entropy produced in the system by irreversible processes (e.g. dissipation ). According to the second law of thermodynamics , no entropy can be destroyed in a closed system. It is therefore true . ${\ displaystyle {\ dot {S}} _ {Q}}$${\ displaystyle {\ dot {S}} _ {M}}$${\ displaystyle {\ dot {S}} _ {irr}}$${\ displaystyle {\ dot {S}} _ {irr} \ geq 0}$

For there is a reversible process , for an irreversible process. ${\ displaystyle {\ dot {S}} _ {irr} = 0}$${\ displaystyle {\ dot {S}} _ {irr}> 0}$

## Entropy balance of the biosphere

The entropy balance equation is used to describe thermodynamic non-equilibrium processes, for example in the context of irreversible thermodynamics and for living beings. These, too, can only lower their entropy by exporting entropy into their environment.

An important system for humans that contains living things is the biosphere . Their entropy balance is determined by the entropy generated within the biosphere and the ability of its interfaces to export entropy into space. It can essentially be represented as an import of short-wave solar energy, which for the most part is reflected back into space in long-wave form. If the entropy generated in the biosphere is greater than can be exported through changing interfaces, then the entropy in the biosphere increases.

Even if the system under consideration contains intelligent living beings, its entropy cannot be reduced through measures and innovations by intelligent beings contained in the system, but only through export.

## Remarks

1. The increase in carbon dioxide in the atmosphere changes the parameters of the interfaces to the entropy export.

## literature

• Axel Kleidon, Ralph D. Lorenz: Non-Equilibrium Thermodynamics and the Production of Entropy. Springer Verlag, Heidelberg 2004, ISBN 3-540-22495-5 .
• W. Schneider, S. Haas: Repetitorium Thermodynamik. 1996, ISBN 3-486-23844-2 , Chapter 8.8: Entropy balance and second law

## Individual evidence

1. Peter Stephan, Karlheinz Schaber, Karl Stephan , Franz Mayinger: Thermodynamik. Basics and technical applications. Volume 1: One- component systems. 19th edition. Springer Verlag, Berlin / Heidelberg 2013, ISBN 978-3-642-30097-4 , pp. 187ff.
2. Leó Szilárd: About the decrease in entropy in a thermodynamic system during interventions by intelligent beings. In: Journal of Physics. Volume 53, Nos. 11-12, November 1929, pp. 840-856. ( Link to abstract . The article is also included in Harvey S. Leff, Andrew F. Rex: Maxwell's Demon. Entropy, Information, Computing. 1989, ISBN 0-691-08727-X )