Can Entropy be Negative

A new state function has been introduced in thermodynamics to indicate the direction and outcome of the spontaneity of a reaction. State functions are those physical properties that help in determining the state of a system like Internal energy (U), Enthalpy (H), Gibbs’s free energy (G), and Entropy (S). State functions are those where the change in the quantity can be calculated by considering the initial amount and the final amount only, irrespective of the path taken by the system, which is represented as a finite change (Δ). In contrast to this, there are path functions that depend on the path used to bring about the change, like work (w).

Spontaneity is the property of being spontaneous which can be applied in general reactions. Reactions can be spontaneous or non-spontaneous, depending on whether they are happening on their own or via an external force like heating, catalyst, etc. Spontaneous reactions tend to happen immediately and are usually fast reactions. Non-spontaneous reactions are mostly slow and need some driving force to push the reaction to the products.

The First Law of Thermodynamics

The first law of thermodynamics explains the relationship between the heat content of the system and the work of the system, which means, heat is absorbed by the system or released by the system, and work is done by the system or done on the system; accordingly, the signs are mentioned:

Work done by the system (-w)

Work done on the system (+w)

Heat absorbed by the system (+q)

The heat evolved by the system (-q)

The first law of thermodynamics does not state anything related to the direction of the reaction.

Briefing the Content

Heat is said to flow only in one direction, that is, from a hotter body to a colder body. All the natural processes like emptying the gas cylinder, heat transfer from a hot coffee cup, etc., occur only in one direction. Such reactions are said to be irreversible reactions that cannot be stopped or reversed unless an external source is used to stop or reverse them. All spontaneous reactions are irreversible and take place only in one direction, and cannot be reversed on their own without external assistance.

Example: Falling of water from a mountain is natural and spontaneous and happens only in one direction, but for the water to move from ground to uphill, we need an energy source. So, a waterfall is spontaneous, but moving water uphill is non-spontaneous. The spontaneity of the reaction is related to the second law of thermodynamics, which explains the direction of the reaction.

The Second Law of Thermodynamics

There are many definitions for the second law of thermodynamics. It is the relation between the heat and work of a system that states that all the heat energy of an isolated system cannot be converted to work. The second law introduces the concept of Entropy, which predicts whether the reaction is forbidden. However, it obeys the law of conservation of energy which is the first law of thermodynamics and provides the necessary criterion for the prediction of spontaneous processes.

Is Entropy a Criterion for Spontaneity?

Entropy (S) is the measure of the disorders of a system. Usually, Entropy can be calculated by considering the Entropy of the system and surroundings and adding together for an irreversible system with a temperature change.

ΔSirr = S syst + S surr

Driving Force for the Spontaneous Process

Consider a reaction with ΔH = 0, which means there is no change in enthalpy (H), but still, the process is spontaneous. To understand this, we can consider mixing two gases in a closed, isolated container where the particles of different gases get mixed, which increases the randomness of the system. For a chemical reaction, we talk about the randomness of atoms and molecules, which differ in the arrangement of reactants and products. If the reaction has greater randomness, then the Entropy is large, and if the randomness is low, then the Entropy is also of a lower value.

When heat is added to the system, particles gain energy and move away from each other freely and randomly in all directions, increasing randomness. So the system at a higher temperature has greater Entropy or randomness. Heat supplied to a system at low temperatures produces greater Entropy than the heat provided at higher temperatures.

ΔS = qrev/T

The overall change in Entropy for a spontaneous process is:

ΔStotal = ΔSsys + ΔSsurr > 0

The Entropy of the spontaneous process is said to be greater than 0, which is a positive value.

Entropy is said to be maximum when the system is at equilibrium, and the change in Entropy is 0.

ΔS = 0

Entropy for a spontaneous process increases until it reaches a maximum and a state called equilibrium, at which the change in Entropy is 0.

For a reversible process, Entropy can be calculated by using the following formula:

ΔSsys= qrev.sys/T

The formula for the reversible and irreversible expansion of gas under isothermal conditions is ΔU = 0, but ΔStotal = ΔSsys + ΔSsurr is not equal to 0. So, ΔS can be used as a criterion to predict reversible and irreversible processes.

Entropy Signs:

Entropy for a spontaneous process is high, which is greater than zero, so it takes up a positive sign, ΔS = +ve.

This means the randomness increases in a spontaneous process.

Example: When ice cubes melt, we always observe them melting quickly without any external assistance to turn into liquid, but the liquid needs some force to make it to the ice form. So, ice to liquid is spontaneous, where particles are ordered in ice and more randomly in liquid water. This process is moving in a direction where the randomness is increasing. So, Entropy is a positive value.

Entropy for a non-spontaneous process is low, which is less than zero, so it takes up a negative sign, ΔS = -ve.

Example: When heating the liquid, it is heated to form a vapour. Liquid particles are more ordered than the vapour form.

Negative entropy means: If the entropy of a system decreases, it means the particles are arranged in a more ordered way. For example, in the freezing process water turns to ice where particles of water flow freely and particles of ice are packed. The change in the system is from a random way to an organised way. In such a case, entropy decreases than the initial and becomes negative. Other processes like condensation of vapours, solidification etc. 

How can negative entropy be achieved?

Natural or spontaneous processes take place on their own but non-spontaneous processes need an external aid to occur. Examples: Water turning to ice is not spontaneous. It needs electrical energy to freeze it using a refrigerator. Similarly, Water from a well to an overhead tank needs electricity to pump it by motor.  In all the non-spontaneous processes, the process happens against the nature where the system turns from random to ordered way which needs external energy and hence entropy decreases and becomes negative in all the unnatural or non-spontaneous processes. 

Conclusion

Entropy is the measure of the disorders of a system. It can be calculated by considering the Entropy of the system and surroundings and adding together for an irreversible system with a temperature change. Entropy can be positive or negative. In a spontaneous process, when Entropy is high, it takes up a positive sign, and in a non-spontaneous process, when Entropy is low, it takes up a negative sign.