Entropy Change Formula

Thermodynamics is the study of the energy changes that occur as a result of temperature and heat variations. It also covers the labor required to convert energy from one form to another. The science of thermodynamics is governed by three laws, the second of which we will address today. The second law of thermodynamics discusses the concept of entropy and states that the universe’s entropy is constantly rising. According to this law, the universe’s entropy can never be negative. So, let’s get a better understanding of entropy and entropy change.

Entropy

Entropy is a measure of disorder or unpredictability. Randomness could apply to the entire world, a single chemical reaction, or even heat transport and exchange. The term disorder refers to the irregularity or lack of uniformity in a thermodynamic system.
Because the value of entropy or Entropy Change depends on the substance present in a thermodynamic system, the letter ‘S’ is used to represent it. Entropy is an intriguing concept because it casts doubt on the idea of complete heat transfer. It aids in the reinterpretation of thermodynamics’ second law.
Entropy is proportional to the degree of disorder in a thermodynamic process; the higher the degree of disorder, the higher the entropy.

To put it another way, entropy shows us how much energy does not convert into labor and instead contributes to the disorder of the system. It is virtually impossible to devote all of one’s energy to work because energy is what allows one to perform labor. This is measured by entropy, a metric.
Entropy cannot be described in a single point and must be measured as a change because the rule of thermodynamics states that energy cannot be created or destroyed but may be changed from one form to another. It is for this reason that the Entropy Change is calculated.

Entropy Change

Entropy Change can be described as a shift in a thermodynamic system’s state of disorder caused by the conversion of heat or enthalpy into work. Entropy is higher in a system with a high degree of disorderliness.
Entropy is a state function factor, which means that its value is independent of the thermodynamic process’s pathway and is solely a determinant of the system’s beginning and final states. The changes in entropy in chemical reactions are caused by the rearranging of atoms and molecules, which alters the system’s initial order. This can result in an increase or decrease in the system’s randomness, and thus in an increase or decrease in entropy.

Entropy Change Formula Thermodynamics

A thermodynamic system’s Entropy Change is denoted by the letter S. Using the change in entropy formula, we can compute the Entropy Change of a chemical reaction or a system:

 ΔS = (Q/T)rev

Where,

The heat transfer to or from the thermodynamic system is denoted by Q.

The absolute temperature is denoted by the letter T.

The S.I unit of entropy J/Kmol.

More about entropy change

With the use of a steam engine, scientist Clausius developed the notion of entropy, and he invented the term entropy since it sounded close to the word energy.

The following change in the entropy equation can be used to signify the formula for Entropy Changes in the Universe:

S_universe = S_system + S_environment

This modification in the entropy formula gives an indication of a process’s or a chemical reaction’s spontaneity.

The entropy of a spontaneous process increases, resulting in S_total being greater than zero.

Let us now look at how the change in entropy changes with various procedures and conditions:

Entropy Change with Temperature

Using the Entropy Change formula, it is evident that when heat transfer occurs at a lower temperature, the change in entropy is greater, and when heat transfer occurs at a higher temperature, the change in entropy is greater.

Entropy Change in a Reversible Process

 The Entropy Change definition applies to a reversible process in conceptual terms. As a result, the reversible process’ entropy change is the same as indicated before.

Changes in Entropy in an Irreversible Process

From a practical standpoint, there is no such thing as an irreversible process. As previously stated, entropy is solely determined by the system’s beginning and ultimate states, regardless of the thermodynamic process’s route. As a result, the change in entropy is independent of the pathway for both irreversible and reversible processes. Because it is an irreversible non-quasi static process, this approach is also utilized to calculate the Entropy Change for an ideal gas.

Entropy’s Characteristics

The following are some of the most essential features of a thermodynamic system’s entropy:

• The propensity of the universe to gravitate towards disorder or unpredictability is known as entropy.
• Entropy is a function of enthalpy or the amount of heat that may be transformed into work.
• The mass of a thermodynamic system affects entropy. It is a broad quality since it is independent of the path of heat exchange or heat conversion.
• The universe’s entropy continues to rise.
• The adiabatic process has constant entropy because the change in entropy is zero.

Sample Problems

Question 1: What is Entropy Change and How Does It Affect You? Define.

Solution:

Entropy In a thermodynamic system, change is the phenomenon that measures the change in disorder or unpredictability. It has to do with the heat or enthalpy conversion that occurs during work. When a thermodynamic system has a lot of randomness, it has a lot of entropy. Entropy is a state function, which implies it is independent of the path taken by the thermodynamic process. The shift in entropy happens as atoms and molecules reorganise themselves from their starting state. This might result in a decrease or rise in the system’s disorder or unpredictability, resulting in a decrease or increase in entropy, respectively.

Question 2: What Characteristics are Associated With Entropy?

Solution:

The following are some of the entropy-related characteristics:

The tendency of the universe to gravitate towards randomness is referred to as entropy.

It’s also known as a heat or enthalpy function that can be converted to work.

The entropy of a thermodynamic system is determined by its mass, and so is independent of the heat exchange channel or heat conversion. This is a large piece of real estate.

The entropy of the universe continues to rise.

An adiabatic process has a constant entropy since the Entropy Change is 0.

Question 3: What is the Fusion Entropy?

Solution:

The entropy increase that occurs when a solid melts into a liquid is known as the entropy of fusion. The entropy grows as the phase changes due to the freedom of movement. It is equal to the fusion enthalpy divided by the fusion temperature. Fusion is connected with Gibbs free energy, which has a negative value unless it occurs, in which case it is always positive. Helium, on the other hand, has negative fusion entropy at temperatures below 0.3 K.

Question 4: What are the Entropy Properties?

Solution:

The following are some of the properties of entropy:

1. It is a broad attribute, implying that it is solely dependent on the mass of a system.
2. The universe’s entropy is always expanding.
3. The entropy of a system can never be zero.
4. An adiabatic thermodynamic system’s entropy remains constant.
5. The change in entropy is inversely proportional to the temperature, meaning that as the temperature rises, the change in entropy decreases, whereas as the temperature falls, the change in entropy increases.

Question 5: At 70°C, a chemical reaction occurs spontaneously. What is the smallest value of S for the reaction if the enthalpy change for the reaction is 15 KJ?

Solution:

Because the reaction occurs at a constant temperature. As a result, qrev = H = 15 KJ = 15000 J

T = 70^οC = (70 + 273)K = 343^ο C

The following formula calculates the change in entropy:

ΔS = (Δq/T)rev = (ΔH/T)rev

ΔS = 15000/343

ΔS = 4.37JK^-1mol^-1.

Question 6: What is the entropy change for the conversion of one gram of ice to water at 237K and one atmospheric pressure? (ΔH_fusion =6.435KJ/mol)

Solution:

ΔH_fusion =6.435 ×1000J/mol 

ΔH_fusion=6435/18 j/g

ΔH_fusion = 357.5 j/g

ΔS_f  = (ΔH_fusion) /T

ΔS_f = 357.5/273

ΔS_f = 1.309JK^-1mol^-1.

Question 7: At 0°C, ΔH⁰_fusion = 5 KJ/mol, change of entropy for freezing of one mole of ice will be?

Solution:

ΔH_fusion = 5 KJ/mol = 5000 J/mol

T_f = 273K

ΔS_f = ΔH_fusion/T_f 

ΔS_f = 5000/273

ΔS_f = 18.31JK^-1mol^-1

Question 8: Calculate the entropy change in the surrounding when one mole of H₂O(l) is formed under standard conditions at 284K. Given  Δ_rH⁰ = -274 KJ mol^-1.

Solution:

H₂ + 1/2 O₂    ⇢ H₂O 

At 284K, when 1 mole of H₂O is formed,274 KJ of heat released. The same amount of heat is absorbed by the surrounding.

q_surr = +274 KJ/mol 

T =284K

ΔS_surr = q_surr/T

ΔS_surr = 274/284

ΔS_surr = 0.96 Jmol^-1 K^-1.