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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).
Since the total change in entropy must always be larger or equal to zero, we obtain the inequality W ≤ − Δ F . {\displaystyle W\leq -\Delta F.} We see that the total amount of work that can be extracted in an isothermal process is limited by the free-energy decrease, and that increasing the free energy in a reversible process requires work ...
Since an entropy is a state function, the entropy change of the system for an irreversible path is the same as for a reversible path between the same two states. [23] However, the heat transferred to or from the surroundings is different as well as its entropy change. We can calculate the change of entropy only by integrating the above formula.
This type of expansion is named after James Prescott Joule who used this expansion, in 1845, in his study for the mechanical equivalent of heat, but this expansion was known long before Joule e.g. by John Leslie, in the beginning of the 19th century, and studied by Joseph Louis Gay-Lussac in 1807 with similar results as obtained by Joule.
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.
The laws of thermodynamics imply the following relations between these two heat capacities (Gaskell 2003:23): = = Here is the thermal expansion coefficient: = is the isothermal compressibility (the inverse of the bulk modulus):
Absolute entropy of strontium. The solid line refers to the entropy of strontium in its normal standard state at 1 atm pressure. The dashed line refers to the entropy of strontium vapor in a non-physical state. The standard entropy change for the formation of a compound from the elements, or for any standard reaction is designated ΔS° form or ...
Reversible isothermal expansion of the gas at the "hot" temperature, T H (isothermal heat addition or absorption). During this step (A to B) the gas is allowed to expand and it does work on the surroundings. The temperature of the gas (the system) does not change during the process, and thus the expansion is isothermic.