page_title: Second law of thermodynamics
section_title: Account given by Clausius
hierarchical_section_title: Second law of thermodynamics / History / Account given by Clausius
caption_attribution_description: Deutsch: Rudolf Clausius
context_page_description: The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time, and is constant if and only if all processes are reversible. Isolated systems spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy.
  The total entropy of a system and its surroundings can remain constant in ideal cases where the system is in thermodynamic equilibrium, or is undergoing a reversible process. In all processes that occur, including spontaneous processes, the total entropy of the system and its surroundings increases and the process is irreversible in the thermodynamic sense. The increase in entropy accounts for the irreversibility of natural processes, and the asymmetry between future and past.
  Historically, the second law was an empirical finding that was accepted as an axiom of thermodynamic theory. Statistical mechanics, classical or quantum, explains the microscopic origin of the law.
  The second law has been expressed in many ways. Its first formulation is credited to the French scientist Sadi Carnot, who in 1824 showed that there is an upper limit to the efficiency of conversion of heat to work in a heat engine.
context_section_description: In 1856, the German physicist Rudolf Clausius stated what he called the "second fundamental theorem in the mechanical theory of heat" in the following form:
  where Q is heat, T is temperature and N is the "equivalence-value" of all uncompensated transformations involved in a cyclical process. Later, in 1865, Clausius would come to define "equivalence-value" as entropy. On the heels of this definition, that same year, the most famous version of the second law was read in a presentation at the Philosophical Society of Zurich on April 24, in which, in the end of his presentation, Clausius concludes:
  The entropy of the universe tends to a maximum.
  This statement is the best-known phrasing of the second law. Because of the looseness of its language, e.g. universe, as well as lack of specific conditions, e.g. open, closed, or isolated, many people take this simple statement to mean that the second law of thermodynamics applies virtually to every subject imaginable. This is not true; this statement is only a simplified version of a more extended and precise description.
  In terms of time variation, the mathematical statement of the second law for an isolated system undergoing an arbitrary transformation is:
  where
  S is the entropy of the system and
  t is time.
  The equality sign applies after equilibration. An alternative way of formulating of the second law for isolated systems is:
   with 
  with  the sum of the rate of entropy production by all processes inside the system. The advantage of this formulation is that it shows the effect of the entropy production. The rate of entropy production is a very important concept since it determines (limits) the efficiency of thermal machines. Multiplied with ambient temperature  it gives the so-called dissipated energy .
  The expression of the second law for closed systems (so, allowing heat exchange and moving boundaries, but not exchange of matter) is:
   with 
  Here
   is the heat flow into the system
   is the temperature at the point where the heat enters the system.
  The equality sign holds in the case that only reversible processes take place inside the system. If irreversible processes take place (which is the case in real systems in operation) the >-sign holds.  If heat is supplied to the system at several places we have to take the algebraic sum of the corresponding terms.
  For open systems (also allowing exchange of matter):
   with 
  Here  is the flow of entropy into the system associated with the flow of matter entering the system. It should not be confused with the time derivative of the entropy. If matter is supplied at several places we have to take the algebraic sum of these contributions.
caption: Rudolf Clausius
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