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Concept
Fundamental thermodynamic relation
Summary
In thermodynamics, the fundamental thermodynamic relation are four fundamental equations which demonstrate how four important thermodynamic quantities depend on variables that can be controlled and measured experimentally. Thus, they are essentially equations of state, and using the fundamental equations, experimental data can be used to determine sought-after quantities like G (Gibbs free energy) or H (enthalpy). The relation is generally expressed as a microscopic change in internal energy in terms of microscopic changes in entropy, and volume for a closed system in thermal equilibrium in the following way.
Here, U is internal energy, T is absolute temperature, S is entropy, P is pressure, and V is volume.
This is only one expression of the fundamental thermodynamic relation. It may be expressed in other ways, using different variables (e.g. using thermodynamic potentials). For example, the fundamental relation may be expressed in terms of the enthalpy H as
in terms of the Helmholtz free energy F as
and in terms of the Gibbs free energy G as
The first law of thermodynamics states that:
where and are infinitesimal amounts of heat supplied to the system by its surroundings and work done by the system on its surroundings, respectively.
According to the second law of thermodynamics we have for a reversible process:
Hence:
By substituting this into the first law, we have:
Letting be reversible pressure-volume work done by the system on its surroundings,
we have:
This equation has been derived in the case of reversible changes. However, since U, S, and V are thermodynamic state functions that depends on only the initial and final states of a thermodynamic process, the above relation holds also for non-reversible changes. If the composition, i.e. the amounts of the chemical components, in a system of uniform temperature and pressure can also change, e.g. due to a chemical reaction, the fundamental thermodynamic relation generalizes to:
The are the chemical potentials corresponding to particles of type .
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Thermodynamic equations
Thermodynamics is expressed by a mathematical framework of thermodynamic equations which relate various thermodynamic quantities and physical properties measured in a laboratory or production process. Thermodynamics is based on a fundamental set of postulates, that became the laws of thermodynamics. One of the fundamental thermodynamic equations is the description of thermodynamic work in analogy to mechanical work, or weight lifted through an elevation against gravity, as defined in 1824 by French physicist Sadi Carnot.
Heat
In thermodynamics, heat is the thermal energy transferred between systems due to a temperature difference. In colloquial use, heat sometimes refers to thermal energy itself. An example of formal vs. informal usage may be obtained from the right-hand photo, in which the metal bar is "conducting heat" from its hot end to its cold end, but if the metal bar is considered a thermodynamic system, then the energy flowing within the metal bar is called internal energy, not heat.
Entropy (statistical thermodynamics)
The concept entropy was first developed by German physicist Rudolf Clausius in the mid-nineteenth century as a thermodynamic property that predicts that certain spontaneous processes are irreversible or impossible. In statistical mechanics, entropy is formulated as a statistical property using probability theory. The statistical entropy perspective was introduced in 1870 by Austrian physicist Ludwig Boltzmann, who established a new field of physics that provided the descriptive linkage between the macroscopic observation of nature and the microscopic view based on the rigorous treatment of large ensembles of microstates that constitute thermodynamic systems.