Entropy - JEE Important Topic

Entropy is a measure of randomness or disorders in a system. The major presence of entropy concepts could be seen in thermodynamics, the study of heat transfer within any system. Entropy is often quantified as absolute entropy or change in entropy. In most thermodynamic applications, change in entropy is of much significance as compared to absolute entropy. Let’s discuss in detail the reasons behind quantifying entropy, and how to find or calculate it in thermodynamic problems. The entropy of a system is a thermodynamic function that is dependent on the state of the system and not on the path followed. 

The Second Law of Thermodynamics and Common Misconceptions about Entropy

The second law of thermodynamics states that the entropy of any closed system will either increase or remain constant, i.e., no decrease in entropy will be observed unless the closed system is disturbed. An increase in temperature will cause the atoms or molecules in a system to move more freely within the system. 

The energy inside any closed system can never decrease although it might be possible through extremely difficult ways to reverse the state of a closed system back to its original state without increasing or decreasing the energy within the system. However, the combination of the entropy of a system and the environment will always increase in an irreversible process. 

One of the common misconceptions about the relationship between the second law of thermodynamics and entropy is that it is not possible for a system to become orderly. However, orderliness, i.e., a decrease in entropy in any system can be achieved through external energy transfers.

Absolute Entropy and Change in Entropy

The absolute entropy of a system is denoted by S and is defined based on the concepts of the third law of thermodynamics. According to the law, the entropy of a system will approach zero as the temperature reaches an absolute value. This is applicable in solid states as a perfect crystalline structure is observed at absolute entropy or at absolute temperature. However, not all solids attain zero entropy at absolute temperature.

Change in entropy is denoted by ΔS. Most of the changes in entropy occur during a transition in the phase of a system and hence are an important quantifiable parameter. Entropy changes are observed during fusion, vaporisation, and the formation of a compound. 

Entropy

Let us discuss how to calculate entropy change. The entropy for a reversible process can be given by:

\[\Delta S=\frac{{{q}_{rev}}}{T}\]

For a spontaneous process, the total change in entropy for the system and the surrounding is given by

\[\Delta {{S}_{total}}=\Delta {{S}_{system}}+\Delta {{S}_{surrounding}}\]

\[\Delta S>0\] for a spontaneous process and it increases till its maximum value and then reaches zero at equilibrium.

Expression for entropy change for reversible process

\[\Delta {{S}_{sys}}=\frac{{{q}_{sys,rev}}}{T}\]

The entropy change of surroundings is

\[\Delta {{S}_{total}}=\Delta {{S}_{sys}}+\left( -\frac{\Delta {{H}_{sys}}}{T} \right)\]

Given above are various changes in entropy formula in thermodynamics also known as entropy equation or entropy formula.

 The absolute value of entropy can be found out assuming any constant or zero value at zero Kelvin.

(G) Gibbs Energy and Spontaneity

Entropy and enthalpy change cannot entirely define the direction of change in the spontaneity of a system. To take care of that a thermodynamic function called Gibbs energy or Gibbs function (G) is used. It is an extensive property, a state function and is given by

$G = H-TS$

The change in Gibbs function is given by

\[\Delta {{G}_{sys}}=\Delta {{H}_{sys}}-T\Delta {{S}_{sys}}-{{S}_{sys}}\Delta T\]

At constant temperature, change is zero. Hence,

\[\Delta {{G}_{sys}}=\Delta {{H}_{sys}}-T\Delta {{S}_{sys}}\]

Usually, the subscript is dropped and the general equation becomes

\[\Delta G=\Delta H-T\Delta S\]

• $\Delta G$ is a measure of spontaneity when the system is at constant temperature and pressure.

• $\Delta G$ is negative for a spontaneous process.

• $\Delta G$ is positive for a non-spontaneous process.

What Is the SI Unit of Entropy?

Entropy is a characteristic of matter and hence is expressed as energy divided by the absolute temperature. Hence, the SI unit of entropy is joules/degree Kelvin, i.e., J/K.

Important Points to Remember While Calculating Entropy

• Being an extensive property of matter, the scale of entropy depends on the extent or size of the system.

• A maximum amount of entropy could be observed in an isolated system.

• Entropy is higher/increases in a system with high temperature and a high amount of chemical reactions.

• The order of entropy for various states of matter is Gas > Liquid > Solid

• The following table gives important insights into the process based on the total change in entropy.

• For a spontaneous, i.e., irreversible reaction, no outside energy source is required to drive the reaction in a particular manner. Due to the nil involvement of external energy, the entropy of the system increases, i.e., $\Delta {{S}_{Total}}>0$.

• Similarly, for a non-spontaneous reaction, an external energy source is required to achieve the required results. In such cases, the entropy of the system decreases due to the involvement of an external source.

• In an equilibrium reaction, no change in disorderliness can be observed, leading to a constant zero change in entropy.

• The change in entropy of a reversible adiabatic process is zero, i.e., \[\Delta {{S}_{~}}=\text{ }0\]  since q = 0. This means that the process is occurring in a constant entropy situation. 

• During an exothermic reaction, \[\Delta {{S}_{surrounding}}\] is positive leading to a positive \[\Delta {{S}_{Total}}\]. Hence exothermic reactions are spontaneous in nature.

• During an endothermic reaction although \[\Delta {{S}_{surrounding}}\] is negative, \[\Delta {{S}_{system}}\] is positive leading to a positive \[\Delta {{S}_{Total}}\]. Hence an endothermic reaction is also spontaneous.

• Change in entropy is a better and more accurate measure of spontaneity as compared to free energy because the former takes into account both the system and the surroundings. 

Summary

Entropy is a quantitative measure of randomness or disorderliness of a system. It considers the temperature or energy changes associated with both the system and the surroundings. The total entropy in any problem is the sum of the change in entropy of the system and the surrounding. Based on the result of a change in entropy, the spontaneity of a system can be determined. The SI Unit of entropy is J/K, and it is an extensive characterisation of the matter.