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An isothermal process is a type of thermodynamic process in which the temperature T of a system remains constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir, and a change in the system occurs slowly enough to allow the system to be continuously adjusted to the temperature of the reservoir through heat exchange (see quasi-equilibrium).
In addition, the total change of entropy in both thermal reservoirs over Carnot cycle is zero too, since the inversion of a heat transfer direction means a sign inversion for the heat transferred during isothermal stages: =, +, = Here we denote the entropy change for a thermal reservoir by , = /, where is either for a hot reservoir or for a ...
The entropy of a given mass does not change during a process that is internally reversible and adiabatic. A process during which the entropy remains constant is called an isentropic process, written Δ s = 0 {\displaystyle \Delta s=0} or s 1 = s 2 {\displaystyle s_{1}=s_{2}} . [ 12 ]
Whether carried out reversible or irreversibly, the net entropy change of the system is zero, as entropy is a state function. During a closed cycle, the system returns to its original thermodynamic state of temperature and pressure. Process quantities (or path quantities), such as heat and work are process dependent.
Mathematically, the absolute entropy of any system at zero temperature is the natural log of the number of ground states times the Boltzmann constant k B = 1.38 × 10 −23 J K −1. The entropy of a perfect crystal lattice as defined by Nernst's theorem is zero provided that its ground state is unique, because ln(1) = 0.
The temperature-entropy conjugate pair is concerned with the transfer of energy, especially for a closed system. An isothermal process occurs at a constant temperature. An example would be a closed system immersed in and thermally connected with a large constant-temperature bath. Energy gained by the system, through work done on it, is lost to ...
If an infinitesimally small amount of heat is supplied to a system in a reversible way then, according to the second law of thermodynamics, the entropy change of the system is given by: d S = δ Q T {\displaystyle dS={\frac {\delta Q}{T}}\,}
This is possible provided the total entropy change of the system plus the surroundings is positive as required by the second law: ΔS tot = ΔS + ΔS R > 0. For the three examples given above: 1) Heat can be transferred from a region of lower temperature to a higher temperature in a refrigerator or in a heat pump. These machines must provide ...