Entropy and Second Law of Thermodynamics: The first law of thermodynamics states that “Energy can neither be created nor destroyed; it can only be transformed from one form to another”

Or “The total mass and energy of an isolated system remain unchanged.”

The first law of thermodynamics establishes a relation between the heat changes and work done by a system, but it doesn’t discuss the direction of the flow of heat. The law could not explain the spontaneity or the feasibility of the reaction. The spontaneity or the disturbance in the system, established by the term ‘entropy’, is taken into account in the second law of thermodynamics. Understanding the Entropy of a system and how it is related to the spontaneity of a system is what the second law of thermodynamics explains in detail.   

However, before proceeding with the explanation for the second law of thermodynamics and what it represents, it is important to understand the Entropy of a system.

What is Entropy in Thermodynamics?

The force that makes the spontaneous reaction proceed in a certain direction is Entropy. The tendency of a system to become disordered is the enthalpy of the system. Greater is the disorder; greater will be the Entropy. 

Entropy is the measurement of randomness in a system. It is denoted by S. The absolute value cannot be measured. Therefore the change in enthalpy \(\left( {\Delta {\text{S}}} \right)\) is only measured during a reaction. It is positive for a spontaneous reaction. It is the energy unavailable for doing work.

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Entropy can be measured from structural irregularity. As solids have a regular arrangement, solids have the lowest Entropy, and due to the maximum irregularity in structure, gases have higher entropy values than the solids. The Entropy of solid, liquid and gaseous state of the same substance can be arranged in the following order

\({{\rm{S}}_{{\rm{sol }}}} < {{\rm{S}}_{{\rm{liq }}}} \ll {{\rm{S}}_{{\rm{gas }}}}\)

Entropy is a state function. It is an extensive property as it depends on the quantity of the substance.

So, the total Entropy for any kind of spontaneous system or process can be given as:

\(\Delta {{\rm{S}}_{{\rm{total }}}} = \Delta {{\rm{S}}_{{\rm{system }}}} + \Delta {{\rm{S}}_{{\rm{surr }}}} > 0\)

According to this, when a system is in an equilibrium position, the Entropy of the system would be maximum, and the change in Entropy, \({\rm{\Delta S = 0}}\)

So, when a system reaches a maximum, at equilibrium, the entropy change becomes zero for that system. Entropy is a state property and can be given in terms of the temperature of the system.

Entropy and Temperature

Providing heat to a system increases the randomness of the system. The randomness of a system is influenced by temperature. At lower temperatures, the randomness is lesser, and at higher temperatures, the randomness of the system is greater.

The change in Entropy of a reversible system, \({\rm{\Delta S,}}\) is given as

\(\Delta {\rm{S}} = {\rm{q}}/{\rm{T}}\)

1. \({\rm{q}}\) is the heat of the reaction and
2. \({\rm{T}}\) is the temperature in Kelvin.

The unit of Entropy is \({\rm{J}}{/^ \circ }{\rm{K}}\) or Calories/degree

If the heat changes occur at constant pressure, then \(\Delta {\rm{S}} = \Delta {\rm{H}}/{\rm{T}}\)

Entropy changes Accompanying Phase Changes

In the process of melting, the Entropy increases, and whilezing, the Entropy decreases. The entropy changes during the phase changes like vapourisation and fusion can be calculated from the enthalpy of vaporisation and enthalpy of fusion, respectively, as given in the formula below:

\(\Delta {{\rm{S}}_{{\rm{vap }}}} = \Delta {{\rm{H}}_{{\rm{vap }}}}/{\rm{T}}\) where \(\Delta {{\rm{H}}_{{\rm{vap }}}}\) is the latent heat of vaporisation

\(\Delta {{\rm{S}}_{{\rm{fusion }}}} = \Delta {{\rm{H}}_{{\rm{fusion }}}}/{\rm{T}}\) where \(\Delta {{\rm{H}}_{{\rm{fusion }}}}\) is the latent heat of fusion

Entropy in Exothermic- Endothermic Reactions

In an exothermic process, \(\Delta {{\rm{S}}_{{\rm{surr}}}}\) is positive, which means more disorder in the surrounding. In an endothermic process, \(\Delta {{\rm{S}}_{{\rm{surr}}}}\) is negative and hence less disorderliness in the surrounding.

Standard Entropy 

The absolute Entropy of a substance at \({25^ \circ }{\rm{C}}(298\;{\rm{K}})\) and \(1\) atmospheric pressure is called the standard Entropy, \({{\rm{S}}^ \circ }.\)

Standard Entropy of formation is given by the formation of \(1\) mole of a compound from the elements under standard conditions.

\({\bf{S}}_{\rm{f}}^0 = {\bf{S}}_{{\rm{products }}}^0 – {\bf{S}}_{{\rm{reactants}}}^0\)

Variation of Entropy with Temperature

For a small change in the state of a system, the entropy change is given by

\(\Delta {\rm{S}} = \Delta {\rm{q}}/{\rm{T}}\)

Entropy and Second Law of Thermodynamics

The second law of thermodynamics is based upon spontaneity and Entropy. The concept that the increase in Entropy leads to a spontaneous change in any system is the basis of the second law of thermodynamics. The second law of thermodynamics explains how a spontaneous exothermic reaction occurs and why they are very common in nature. Since heat is released in an exothermic reaction, there is an increase in disorder in the surroundings, and therefore, the overall entropy change becomes positive, thereby making the reaction spontaneous.

Second Law of Thermodynamics

Consider a chemical reaction:

\({\rm{NaOH}} + {\rm{HCl}} – > {\rm{NaCl}} + {{\rm{H}}_2}{\rm{O}}\)

The forward reaction here is spontaneous. However, the backward reaction between \({\rm{NaCl}}\) and \({{\rm{H}}_2}{\rm{O}}\) does not take place on its own unless reaction conditions are changed. There are several such reactions, where one side of the reaction is spontaneous while the other side is not. Hence, the second law of thermodynamics can be written as:

‘All spontaneous processes or those which naturally occur are thermodynamically irreversible.’

As we mentioned earlier, the reverse reaction might require force and changed conditions to occur. Hence, the second law of thermodynamics can be written as:

‘A spontaneous process cannot be reversed without the help of external force’.

Also, since the heat or any energy applied to a system is not fully utilised, since some of it goes into changes that occur in a system, the law can also be written as:

‘The complete conversion of heat into work is not possible without leaving some effects somewhere in the system’.

Also, according to the second law of thermodynamics, all spontaneous processes are always accompanied by some or net increase in the Entropy of the system, and hence, the Entropy of a system is continuously increasing.

As the first law of thermodynamics, there are several ways in which the second law can be stated. 

Hence, the second law of thermodynamics can be written as:

 “In any spontaneous process, there is always an increase in the entropy of the universe”

“The entropy of the universe is increasing”

\({\rm{\Delta }}{{\rm{S}}_{{\rm{universe }}}}{\rm{ = \Delta }}{{\rm{S}}_{{\rm{sys }}}}{\rm{ + \Delta }}{{\rm{S}}_{{\rm{surr }}}}({\rm{Always}} > 0)\)

\({\rm{\Delta }}{{\rm{S}}_{{\rm{sys }}}}{\rm{ = 0}}\) for a system in equilibrium

\(\Delta {{\rm{S}}_{{\rm{sys}} \ne }}0\) for an irreversible process

So, for a spontaneous and irreversible system, the value \(\Delta {\rm{S}} > 0.\)

From the value of \(\Delta {{\rm{S}}_{{\rm{sys,}}}}\) it is possible to predict whether the reaction is feasible or not.

In the reaction \({{\rm{H}}_{2({\rm{g}})}} \to 2{{\rm{H}}_{{{({\rm{g}})}^,}}}\) the number of particles increases (from \(1\) mole of molecular hydrogen to \(2\) moles of atomic hydrogen), leading to an increase in Entropy.

Importance of Second Law of Thermodynamics

The driving force for a spontaneous process is an increase in the Entropy of the universe. Nature proceeds towards the state that has the highest probability of existing. Hence, the second law predicts the feasibility of any chemical reaction. It, therefore, helps in deciding if a reaction can take place or not spontaneously. It also shows or indicates the direction of heat flow in a reaction. 

Example:

i) If a hot object and cold object are kept in contact, the heat from the hot object transfers to the cold object until both are of the same temperature. i.e., the heat transfer from hot to cold objects is spontaneous.

ii) Melting of ice.

Kelvin-Planck Statement of the Second Law of Thermodynamics

Kelvin and Plank gave a statement for the second law of thermodynamics. According to them,

 ‘It is impossible to use a cyclic process to transfer heat from a reservoir and to convert it into work without transferring at the same time a certain amount of heat from a hotter to a colder part of the body.’

In a heat engine, the efficiency can be calculated as the fraction of heat absorbed by an engine that can be converted to work. The Kelvin-Planck statement actually talks about an ideal heat engine that extracts heat and converts it completely into work. Hence, the Kelvin-Planck statement gives an ideal situation wherein the second law of thermodynamics can be applied. However, it is practically not possible to do so in the real world.

So, it can be represented mathematically as follows:

The thermal efficiency of the engine can be calculated as (represented by ‘eta’)

\({\rm{\eta = net}}\,{\rm{work}}\,{\rm{done}}\left( {{{\rm{q}}_{\rm{1}}}{\rm{ – }}{{\rm{q}}_{\rm{2}}}} \right){\rm{/total}}\,{\rm{amount}}\,{\rm{of}}\,{\rm{heat}}\,{\rm{absorbed}}\,{\rm{by}}\,{\rm{the}}\,{\rm{substance}}\left( {{{\rm{q}}_{\rm{1}}}} \right) \)
\(= {\rm{w}}/{\rm{q}} = \left( {{{\rm{T}}_2} – {{\rm{T}}_1}} \right)/{{\rm{T}}_2}\)

An ideal situation or \(100\% \) efficiency would make \({\rm{\eta = 1}}\) Since \(\left( {{{\rm{T}}_{\rm{2}}}{\rm{ – }}{{\rm{T}}_{\rm{1}}}} \right){\rm{/}}{{\rm{T}}_{\rm{2}}}\) is less than \(1,\) the efficiency is always less than \(1.\) Some heat is lost during the process.

Summary

Entropy is an important thermodynamic quantity that could account for the spontaneity of a system. It is a measure of randomness in a system. The Entropy of gases is more compared to that of liquids and solids. It is an extensive property and a state function. The entropy of the universe increases. It can be calculated when heat changes accompanying a reaction is known. The feasibility and reversibility of the reaction can be found out using Entropy, and this is shown by the second law of thermodynamics, which is based upon the fact that the reactions occur spontaneously in nature due to an entity called Entropy.

FAQs on Entropy and Second Law of Thermodynamics

Q.1. What is Entropy in thermodynamics?
Ans: Entropy is the measurement of randomness in a system.

Q.2. What does the second law of thermodynamics state about Entropy?
Ans: The second law of thermodynamics state that “In any spontaneous process, there is always an increase in the entropy of the universe.”

Q.3. What are the limitations of the second law of thermodynamics?
Ans: The second law does not say anything about the direction of the flow of heat.

Q.4. What are the applications of the second law of thermodynamics?
Ans: i) It helps to predict the feasibility of the reaction.
ii) It provides the direction of the flow of heat (To the system-Endothermic; from the system- Exothermic).

Q.5. What is the second law of the thermodynamics equation?
Ans: \({\rm{\Delta }}{{\rm{S}}_{{\rm{Universe }}}}{\rm{ > 0}}\)

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