Entropy, the measure of a system’s thermal energy per unit temperature that is unavailable for doing useful work. Because work is obtained from ordered molecular motion, the amount of entropy is also a measure of the molecular disorder, or randomness, of a system. The concept of entropy provides deep insight into the direction of spontaneous change for many everyday phenomena. Its introduction by the German physicist Rudolf Clausius in 1850 is a highlight of 19th-century physics.

In statistical mechanics, S° is an extensive property of a thermodynamic system. It is strictly related to the number Ω of imperceptible compositions (known as microstates) that are steady with the macroscopic capacities that characterize the system (such as its volume, pressure, and temperature). S° expresses the number Ω of different compositions that a system delineated by macroscopic variables could assume. Under the guess that each microstate is equally probable, the entropy S is the natural logarithm of the number of microstates, multiplied by the Boltzmann constant kB.

Entropy Equation/Formula

Entropy is a thermodynamic function used to measure the randomness or disorder of a system. For example, the S° of a solid, where the particles are not free to move, is less than the S° of a gas, where the particles will fill the container. Scientists have concluded that if a process is to be spontaneous, the S° of that process must increase. This includes the S° of the system and the S° of the surroundings.


Entropy can be calculated using many different equations:

  • If the process is at a constant temperature then, where ΔS is the change in entropy
    Entropy Equation Formula
    Entropy Equation Formula

    , qrev is the reverse of the heat, and T is the Kelvin temperature.

  • If the reaction is known, then ΔSrxn can be calculated using a table of standard entropy values.
    Total Entropy Change
    Total Entropy Change
  • Gibbs free energy (ΔG) and enthalpy (ΔH) can also be used to calculate ΔS.
Gibbs Free Energy
Gibbs Free Energy

Entropy Definition

There are two equivalent definitions of entropy: the thermodynamic definition and the statistical mechanic’s definition. Historically, the classical thermodynamics definition developed first. In the classical thermodynamics viewpoint, the microscopic details of a system are not considered. Instead, the behavior of a system is described in terms of a set of empirically defined thermodynamic variables, such as temperature, pressure, entropy, and heat capacity. The classical thermodynamics description assumes a state of equilibrium although more recent attempts have been made to develop useful definitions of entropy in nonequilibrium systems as well.

The statistical definition of S° and other thermodynamic properties were developed later. In this viewpoint, thermodynamic properties are defined in terms of the statistics of the motions of the microscopic constituents of a system modeled at first classically, e.g. Newtonian particles constituting a gas, and later quantum-mechanically.

Molar Entropy Equation

The standard molar entropy is usually given the symbol S° and has units of joules per mole kelvin (J mol−1 K−1). Unlike the standard enthalpies of formation, the value of S° is absolute. That is, an element in its standard state has a definite, nonzero value of S at room temperature. The S° of a pure crystalline structure can be 0 J mol−1 K−1 only at 0 K, according to the third law of thermodynamics. However, this presupposes that the material forms a ‘perfect crystal’ without any frozen in S° (defects, dislocations), which is never completely true because crystals always grow at finite temperature. However, this residual entropy is often quite negligible.

If a mole of substance were at 0 K, then warmed by its surroundings to 298 K, its total molar entropy would be the addition of all N individual contributions:

{\displaystyle S^{\circ }=\sum _{k=1}^{N}\Delta S_{k}=\sum _{k=1}^{N}\int {\frac {dq_{k}}{T}}\,dT}S^\circ = \sum_{k=1}^N \Delta S_k =\sum_{k=1}^N \int \frac{dq_k}{T} \, dT
Here, dqk/T represents a very small exchange of heat energy at temperature T. The total molar entropy is the sum of many small changes in molar entropy, where each small change can be considered a reversible process.

What Is the Concept Of S°?

S°, The Measure Of A System’s Thermal Energy Per Unit Temperature That Is Unavailable For Doing Useful Work. Because Work Is Obtained From Ordered Molecular Motion, The Amount Of S° Is Also A Measure Of The Molecular Disorder, Or Randomness, Of A System.

What Is S° With Example?

S° Is A Measure Of The Energy Dispersal In The System. We See Evidence That The Universe Tends Toward Highest S Many Places In Our Lives. A Campfire Is An Example Of S. The Solid Wood Burns And Becomes Ash, Smoke, And Gases, All Of Which Spread Energy Outwards More Easily Than The Solid Fuel.

What Is The Unit Of Entropy?

The Si Unit For S° Is Joules Per Kelvin (J/K). A More Positive Value Of S Means A Reaction Is More Likely To Happen Spontaneously.

What Does The Second Law Of Thermodynamics State?

The Second Law Of Thermodynamics States That The State Of S° Of The Entire Universe, As An Isolated System, Will Always Increase Over Time. The Second Law Also States That The Changes In The S° In The Universe Can Never Be Negative.

What Is The Symbol For Entropy Change?

It Is Usually Denoted By The Symbol S This Is Attributed To The Work Of Clausius In 1865 When He Gave Irreversible Heat Loss Which He Had Previously Called “Equivalence-value” A Name.