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.
During the latter half of the 19th century, physicists such as Rudolf Clausius, Peter Guthrie Tait, and Willard Gibbs worked to develop the concept of a thermodynamic system and the correlative energetic laws which govern its associated processes.
A thermodynamic system may be composed of many subsystems which may or may not be "insulated" from each other with respect to the various extensive quantities.
The second law of thermodynamics specifies that the equilibrium state that it moves to is in fact the one with the greatest entropy.
Once we know the entropy as a function of the extensive variables of the system, we will be able to predict the final equilibrium state.
As a simple example, consider a system composed of a number of k different types of particles and has the volume as its only external variable.
The fundamental thermodynamic relation may then be expressed in terms of the internal energy as: Some important aspects of this equation should be noted: (Alberty 2001), (Balian 2003), (Callen 1985) By the principle of minimum energy, the second law can be restated by saying that for a fixed entropy, when the constraints on the system are relaxed, the internal energy assumes a minimum value.
For each such potential, the relevant fundamental equation results from the same Second-Law principle that gives rise to energy minimization under restricted conditions: that the total entropy of the system and its environment is maximized in equilibrium.
The intensive parameters give the derivatives of the environment entropy with respect to the extensive properties of the system.
Because all of the natural variables of the internal energy U are extensive quantities, it follows from Euler's homogeneous function theorem that Substituting into the expressions for the other main potentials we have the following expressions for the thermodynamic potentials: Note that the Euler integrals are sometimes also referred to as fundamental equations.
It follows that for a simple system with r components, there will be r+1 independent parameters, or degrees of freedom.
For example, a simple system with a single component will have two degrees of freedom, and may be specified by only two parameters, such as pressure and volume for example.
Maxwell relations are equalities involving the second derivatives of thermodynamic potentials with respect to their natural variables.
They follow directly from the fact that the order of differentiation does not matter when taking the second derivative.
Second derivatives of thermodynamic potentials generally describe the response of the system to small changes.
For the case of a single component system, there are three properties generally considered "standard" from which all others may be derived: These properties are seen to be the three possible second derivative of the Gibbs free energy with respect to temperature and pressure.
Properties such as internal energy, entropy, enthalpy, and heat transfer are not so easily measured or determined through simple relations.
The change in entropy with respect to pressure at a constant temperature is the same as the negative change in specific volume with respect to temperature at a constant pressure, for a simple compressible system.
It is significant to any phase change process that happens at a constant pressure and temperature.
It also allows us to determine the specific volume of a saturated vapor and liquid at that provided temperature.
According to this relation, the difference between the specific heat capacities is the same as the universal gas constant.