Second Law of Thermodynamics

A Second Law of Thermodynamics is physical phenomena law which states that entropy of closed physical system is always increasing.

• AKA: Carnot's Principle.
• Context
  • For a reversible process the total entropy of the system remains a constant.
  • For a irreversible process the total entropy of the system must increase.
• Example(s)
  • Carnot Cycle.
• Counter-Example(s)
  • First Law of Thermodynamics.
  • Zero Law of Thermodynamics.
  • Third Law of Thermodynamics.
• See: Entropy, Carnot Efficiency, Laws Of Thermodynamics, Perpetual Motion Machines, Thermodynamics, Physical System, Maxwell's Demon Thought Experiment.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/second_law_of_thermodynamics Retrieved:2015-12-19.
  • The second law of thermodynamics states that in every real process the sum of the entropies of all participating bodies is increased. In the idealized limiting case of a reversible process, this sum remains unchanged. The increase in entropy accounts for the irreversibility of natural processes, and the asymmetry between future and past.

    While often applied to more general processes, the law technically pertains to an event in which bodies initially in thermodynamic equilibrium are put into contact and allowed to come to a new equilibrium. This equilibration process involves the spread, dispersal, or dissipation of matter or energy and results in an increase of entropy.

    The second law is an empirical finding that has been accepted as an axiom of thermodynamic theory. Statistical thermodynamics, 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 in 1824 (see Timeline of thermodynamics).

• (NASA Website, 2015) ⇒ https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
  • Clasius, Kelvin, and Carnot proposed various forms of the second law to describe the particular physics problem that each was studying. The description of the second law stated on this slide was taken from Halliday and Resnick's textbook, "Physics". It begins with the definition of a new state variable called entropy. Entropy has a variety of physical interpretations, including the statistical disorder of the system, but for our purposes, let us consider entropy to be just another property of the system, like enthalpy or temperature.

The second law states that there exists a useful state variable called entropy S. The change in entropy [math]\displaystyle{ \delta S }[/math] is equal to the heat transfer [math]\displaystyle{ \delta Q }[/math] divided by the temperature T:

[math]\displaystyle{ \delta S = \frac{\delta Q}{T} }[/math]

For a given physical process, the combined entropy of the system and the environment remains a constant if the process can be reversed. If we denote the initial and final states of the system by "i" and "f":

[math]\displaystyle{ S_f = S_i \quad\textrm{(reversible process)} }[/math]

An example of a reversible process is ideally forcing a flow through a constricted pipe. Ideal means no boundary layer losses. As the flow moves through the constriction, the pressure, temperature and velocity change, but these variables return to their original values downstream of the constriction. The state of the gas returns to its original conditions and the change of entropy of the system is zero. Engineers call such a process an isentropic process. Isentropic means constant entropy.

The second law states that if the physical process is irreversible, the combined entropy of the system and the environment must increase. The final entropy must be greater than the initial entropy for an irreversible process:

[math]\displaystyle{ Sf \gt Si \quad\textrm{(irreversible process)} }[/math]

An example of an irreversible process is the problem discussed in the second paragraph. A hot object is put in contact with a cold object. Eventually, they both achieve the same equilibrium temperature. If we then separate the objects they remain at the equilibrium temperature and do not naturally return to their original temperatures. The process of bringing them to the same temperature is irreversible.

2012

• (Tong, 2012) ⇒ David Tong. (2012). “Statistical Physics". University of Cambridge Part II Mathematical Tripos. http://www.damtp.cam.ac.uk/user/tong/statphys/sp.pdf
  • Pages 6 - 8

2010

• (Halliday et al., 2010) ⇒ David Halliday, Robert Resnick, and Jearl Walker. “Fundamentals of physics extended". John Wiley & Sons, 2010.

2005

• (Hyperphysics Encyclopedia, 2005) ⇒ http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/seclaw.html#c1
  • The second law of thermodynamics is a general principle which places constraints upon the direction of heat transfer and the attainable efficiencies of heat engines. In so doing, it goes beyond the limitations imposed by the first law of thermodynamics. It's implications may be visualized in terms of the waterfall analogy. If you constrained to put your waterwheel half-way up the waterfall, then you can extract most half of the energy available. If a 600 K heat engine must exhaust heat at 300 K it can be at most 50% efficient. The maximum efficiency which can be achieved is the Carnot efficiency.

1998

• (Principia Cybernetica Web, 2005) ⇒ http://pespmc1.vub.ac.be/ENTRTHER.html
  • The principal energy laws that govern every organization are derived from two famous laws of thermodynamics. The second law, known as Carnot's principle, is controlled by the concept of entropy(...) The two principal laws of thermodynamics apply only to closed systems, that is, entities with which there can be no exchange of energy, information, or material. The universe in its totality might be considered a closed system of this type; this would allow the two laws to be applied to it.

The first law of thermodynamics says that the total quantity of energy in the universe remains constant. This is the principle of the conservation of energy. The second law of thermodynamics states that the quality of this energy is degraded irreversibly. This is the principle of the degradation of energy.

(...)There seems to be a contradiction between the first and second principles(...) Statistical theory provides the answer. Heat is energy; it is kinetic energy that results from the movement of molecules in a gas or the vibration of atoms in a solid. In the form of heat this energy is reduced to a state of maximum disorder in which each individual movement is neutralized by statistical laws. Potential energy, then, is organized energy; heat is disorganized energy. And maximum disorder is entropy. The mass movement of molecules (in a gas, for example) will produce work (drive a piston). But where motion is ineffective on the spot and headed in all directions at the same time, energy will be present but ineffective. One might say that the sum of all the quantities of heat lost in the course of all the activities that have taken place in the universe measures the accumulation of entropy.

One can generalise further. Thanks to the mathematical relation between disorder and probability, it is possible to speak of evolution toward an increase in entropy by using one or the other of two statements: "left to itself, an isolated system tends toward a state of maximum disorder" or "left to itself, an isolated system tends toward a state of higher probability."

1963

• (Feynman et al., 1963) ⇒ Richard P. Feynman, Robert B. Leighton and Matthew Sands (1963, 1977, 2006, 2010, 2013) "The Feynman Lectures on Physics": New Millennium Edition is now available online by the California Institute of Technology, Michael A. Gottlieb, and Rudolf Pfeiffer ⇒ http://www.feynmanlectures.caltech.edu/
  • Second law:A process whose only net result is to take heat from a reservoir and convert it to work is impossible. No heat engine taking heat Q1 from T1 and delivering heat Q2 at T2 can do more work than a reversible engine, for which

[math]\displaystyle{ W=Q1−Q2=Q1(\frac{T1−T2}{T1}) }[/math]

The entropy of a system is defined this way:

(a)If heat [math]\displaystyle{ \Delta Q }[/math] is added reversibly to a system at temperature T, the increase in entropy of the system is [math]\displaystyle{ \Delta S=\Delta Q/T }[/math]

(b)At T=0, S=0 </math>(third law).

In a reversible change, the total entropy of all parts of the system (including reservoirs) does not change. In irreversible change, the total entropy of the system always increases.

1874

• (Boltzmann, 1874).

1874

• (Carnot, 1824).

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