# Entropy – Definition, Formula & More

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

, 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
• Gibbs free energy (ΔG) and enthalpy (ΔH) can also be used to calculate ΔS.

### 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: 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.