WHAT IS LAW OF ENTROPY?

LAW OF ENTROPY

The second law of thermodynamics states that the total entropy of an isolated system can only increase over time. It can remain constant in ideal cases where the system is in a steady state (equilibrium) or undergoing a reversible process.

In statistical mechanics, entropy (usual symbol S) is related to the number of microscopic configurations Ω that a thermodynamic system can have when in a state as specified by some macroscopic variables. Specifically, assuming for simplicity that each of the microscopic configurations is equally probable, the entropy of the system is the natural logarithm of that number of configurations, multiplied by the Boltzmann constant kB. Formally,

This is consistent with 19th century formulas for entropy in terms of heat and temperature, as discussed below. Boltzmann's constant, and therefore entropy, have dimensions of energy divided by temperature.

For example, gas in a container with known volume, pressure, and energy could have an enormous number of possible configurations of the collection of individual gas molecules. At equilibrium, each instantaneous configuration of the gas may be regarded as random. Entropy may be understood as a measure of disorder within a macroscopic system. The second law of thermodynamics states that an isolated system's entropy never decreases. Such systems spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy. Non-isolated systems may lose entropy, provided their environment's entropy increases by at least that amount. Since entropy is a function of the state of the system, a change in entropy of a system is determined by its initial and final states. This applies whether the process is reversible or irreversible. However, irreversible processes increase the combined entropy of the system and its environment.

In the mid-19th century, the change in entropy (ΔS) of a system undergoing a thermodynamically reversible process was defined by Rudolf Clausius as:

,

where T is the absolute temperature of the system, dividing an incremental reversible transfer of heat into that system (δQrev). (If heat is transferred out the sign would be reversed giving a decrease in entropy of the system.) The above definition is sometimes called the macroscopic definition of entropy because it can be used without regard to any microscopic description of the contents of a system. The concept of entropy has been found to be generally useful and has several other formulations. Entropy was discovered when it was noticed to be a quantity that behaves as a function of state, as a consequence of the second law of thermodynamics.

Entropy is an extensive property. It has the dimension of energy divided by temperature, which has a unit of joules per kelvin (J K−1) in the International System of Units (or kg m2 s−2 K−1 in terms of base units). But the entropy of a pure substance is usually given as an intensive property—either entropy per unit mass (SI unit: J K−1 kg−1) or entropy per unit amount of substance (SI unit: J K−1 mol−1).

The absolute entropy (S rather than ΔS) was defined later, using either statistical mechanics or the third law of thermodynamics, an otherwise arbitrary additive constant is fixed such that the entropy of a pure substance at absolute zero is zero. In statistical mechanics this reflects that the ground state of a system is generally non-degenerate and only one microscopic configuration corresponds to it.

The fundamental thermodynamic relation

The entropy of a system depends on its internal energy and its external parameters, such as its volume. In the thermodynamic limit, this fact leads to an equation relating the change in the internal energy U to changes in the entropy and the external parameters. This relation is known as the fundamental thermodynamic relation. If external pressure Pbears on the volume V as the only external parameter, this relation is

Since both internal energy and entropy are monotonic functions of temperature T, implying that the internal energy is fixed when one specifies the entropy and the volume, this relation is valid even if the change from one state of thermal equilibrium to another with infinitesimally larger entropy and volume happens in a non-quasistatic way (so during this change the system may be very far out of thermal equilibrium and then the entropy, pressure and temperature may not exist).

The fundamental thermodynamic relation implies many thermodynamic identities that are valid in general, independent of the microscopic details of the system. Important examples are the Maxwell relations and the relations between heat capacities.