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  2. Spontaneous process - Wikipedia

    en.wikipedia.org/wiki/Spontaneous_process

    When ΔS > 0 and ΔH < 0, the process is always spontaneous as written. When ΔS < 0 and ΔH > 0, the process is never spontaneous, but the reverse process is always spontaneous. When ΔS > 0 and ΔH > 0, the process will be spontaneous at high temperatures and non-spontaneous at low temperatures. When ΔS < 0 and ΔH < 0, the process will be ...

  3. Rubber band experiment - Wikipedia

    en.wikipedia.org/wiki/Rubber_band_experiment

    The T-V diagram of the rubber band experiment. The decrease in the temperature of the rubber band in a spontaneous process at ambient temperature can be explained using the Helmholtz free energy = where dF is the change in free energy, dL is the change in length, τ is the tension, dT is the change in temperature and S is the entropy.

  4. Thermodynamic free energy - Wikipedia

    en.wikipedia.org/wiki/Thermodynamic_free_energy

    Thus, a negative value of the change in free energy is a necessary condition for a process to be spontaneous; this is the most useful form of the second law of thermodynamics in chemistry. In chemical equilibrium at constant T and p without electrical work, dG = 0.

  5. Self-organization - Wikipedia

    en.wikipedia.org/wiki/Self-organization

    Self-organization, also called spontaneous order in the social sciences, is a process where some form of overall order arises from local interactions between parts of an initially disordered system. The process can be spontaneous when sufficient energy is available, not needing control by any external agent.

  6. Spontaneous order - Wikipedia

    en.wikipedia.org/wiki/Spontaneous_order

    Spontaneous order, also named self-organization in the hard sciences, is the spontaneous emergence of order out of seeming chaos. The term "self-organization" is more often used for physical changes and biological processes, while "spontaneous order" is typically used to describe the emergence of various kinds of social orders in human social networks from the behavior of a combination of self ...

  7. Helmholtz free energy - Wikipedia

    en.wikipedia.org/wiki/Helmholtz_free_energy

    and thus for a system kept at constant temperature and volume and not capable of performing electrical or other non-PV work, the total free energy during a spontaneous change can only decrease. This result seems to contradict the equation dF = −S dT − P dV, as keeping T and V constant seems to imply dF = 0, and hence F = constant.

  8. Third law of thermodynamics - Wikipedia

    en.wikipedia.org/wiki/Third_law_of_thermodynamics

    In the limit T 00 this expression diverges, again contradicting the third law of thermodynamics. The conflict is resolved as follows: At a certain temperature the quantum nature of matter starts to dominate the behavior. Fermi particles follow Fermi–Dirac statistics and Bose particles follow Bose–Einstein statistics. In both cases the ...

  9. Activation energy - Wikipedia

    en.wikipedia.org/wiki/Activation_energy

    In transition state theory, a more sophisticated model of the relationship between reaction rates and the transition state, a superficially similar mathematical relationship, the Eyring equation, is used to describe the rate constant of a reaction: k = (k B T / h) exp(−ΔG ‡ / RT). However, instead of modeling the temperature dependence of ...