The Clausius theorem, also called the Clausius inequality, states that for a thermodynamic system exchanging heat with external thermal reservoirs while undergoing a thermodynamic cycle, the entropy of those reservoirs increases or stays the same and never decreases per cycle. In the special case of a reversible process the inequality becomes an equality, and that reversible case is used to introduce the state function known as entropy. The theorem follows from applying the second law of thermodynamics at each infinitesimal stage of heat transfer, and its underlying statement is that heat spontaneously flows from a hot body to a cooler one and never the reverse.
Facts
StatementFor a thermodynamic system exchanging heat with external reservoirs while undergoing a thermodynamic cycle, the cyclic integral of heat transferred divided by reservoir temperature is less than or equal to zero, with equality only in the reversible case, so the entropy of the reservoirs never decreases per cycle. 1 Classification
Statement Form Connections
Has Statement Form
In Branch
Source Clausius theorem, Wikipedia
Proved By
Source Clausius theorem, Wikipedia
Sources
1. Clausius theorem, Wikipedia
Introduction, opening paragraph
The Clausius theorem, also known as the Clausius inequality, states that for a thermodynamic system (e.g. heat engine or heat pump) exchanging heat with external thermal reservoirs and undergoing a thermodynamic cycle, the following inequality holds.
History section
What is now known as the Clausius theorem was first published in 1862 in Clausius' sixth memoir, "On the Application of the Theorem of the Equivalence of Transformations to Interior Work".
Lead section, statement-form reference
The Clausius statement states that it is impossible to construct a device whose sole effect is the transfer of heat from a cool reservoir to a hot reservoir.
In Branch: Mathematical Physics, Lead
The Clausius theorem, also known as the Clausius inequality, states that for a thermodynamic system
In Group: Statistical Mechanics and Thermodynamics, Lead section
inequality is a consequence of applying the second law of thermodynamics at each infinitesimal stage of heat transfer.
Proved By: Rudolf Clausius, Lead
It was developed by Rudolf Clausius who intended to explain the relationship between the heat flow in a system and the entropy of the system and its surroundings
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