# Enthalpy vs. Entropy: Difference Between Enthalpy and Entropy, Thermodynamics Laws

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Posted by Osman Gezer, 2/15/24

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In the field of thermodynamics, two important concepts that are frequently used to understand heat and energy are enthalpy and entropy. Enthalpy represents the heat content of a system, while entropy measures the degree of disorder in a system. Understanding the difference between these two concepts is crucial for comprehending thermodynamic processes and their relationship to energy transfer.

## What is Enthalpy?

Enthalpy is a measure of the total heat content of a system. It accounts for the heat that can flow into or out of the system during a chemical reaction. Changes in enthalpy, also known as enthalpy changes, are important in understanding the energy changes that occur during a chemical reaction. Enthalpy is defined as the sum of the internal energy of the system and the product of the pressure and volume of the system.

## What is Entropy?

Entropy is a measure of the randomness or disorder in a system. It quantifies the number of ways in which the molecules in a system can be arranged. If the molecules in a system are more random, the entropy of the system will be higher. Conversely, if the molecules are more ordered, the entropy will be lower. Entropy is a function of the quantity of heat and is related to the availability of energy for conversion into work.

## What is Thermodynamics?

Before delving deeper into the differences between enthalpy and entropy, it’s important to understand the field of thermodynamics. Thermodynamics is the study of the relationships between heat, work, and energy. It provides a framework for understanding and predicting the behavior of physical systems, particularly in terms of energy transfer and conversion.

Thermodynamics is governed by several fundamental laws, including the laws of conservation of energy and the increase of entropy. These laws establish the principles that guide the behavior of energy in various systems and processes.

## Enthalpy And Entropy In Thermodynamics

Enthalpy and entropy are both important concepts in thermodynamics and play a significant role in understanding energy transfer and conversion. Enthalpy is particularly useful in studying heat transfer and chemical reactions, while entropy helps to explain the direction of energy flow and the tendency of systems to increase in disorder.

In thermodynamics, enthalpy is represented by the symbol “H,” while entropy is represented by the symbol “S.” Changes in enthalpy are typically denoted as ΔH, while changes in entropy are denoted as ΔS. These changes are often measured under standard conditions to allow for easier comparison and analysis.

## Distinction Between Enthalpy and Entropy

To better understand the differences between enthalpy and entropy, let’s examine their key characteristics:

It is important to note that while enthalpy and entropy are distinct concepts, they are interconnected and play complementary roles in thermodynamics. Changes in enthalpy and entropy influence the direction and feasibility of processes, and their study is crucial for understanding energy transformations.

### Thermodynamics Laws

To gain a deeper understanding of the relationship between enthalpy and entropy, it is necessary to explore the laws of thermodynamics. These laws provide fundamental principles that govern energy transfer and conversion. The two most significant laws in thermodynamics are:

1. The First Law of Thermodynamics: This law, also known as the law of conservation of energy, states that energy cannot be created or destroyed; it can only be converted from one form to another. In the context of enthalpy and entropy, this law helps explain the conservation of energy during chemical reactions and energy transfer.
2. The Second Law of Thermodynamics: This law states that the entropy of an isolated system will always tend to increase over time. In other words, natural processes tend to move towards a state of higher disorder or randomness. This law is also known as the law of entropy or the law of disorder.

The second law of thermodynamics has profound implications for the feasibility and direction of processes. It helps explain why certain processes occur spontaneously, while others require external intervention. The increase in entropy is a measure of the overall randomness or disorder within a system and its surroundings.

### Relationship between Enthalpy and Entropy

Enthalpy and entropy are related to each other through the concept of Gibbs free energy (G). Gibbs free energy is a thermodynamic potential that combines the effects of enthalpy and entropy to determine the feasibility and direction of a process.

The relationship between enthalpy (H), entropy (S), and Gibbs free energy (G) is described by the equation:

ΔG = ΔH – TΔS

In this equation, ΔG represents the change in Gibbs free energy, ΔH represents the change in enthalpy, ΔS represents the change in entropy, and T represents the temperature.

If ΔG is negative, the process is spontaneous and can occur without external intervention. If ΔG is positive, the process is non-spontaneous and requires external energy input to occur. If ΔG is zero, the system is at equilibrium.

The relationship between enthalpy, entropy, and Gibbs free energy allows us to predict the feasibility and direction of processes based on the values of ΔH, ΔS, and temperature. It provides valuable insights into the energetics of chemical reactions and other thermodynamic processes.

### Examples of Enthalpy

To further illustrate the concept of enthalpy, let’s consider a few examples:

1. Combustion of a fuel: When a fuel such as gasoline or natural gas undergoes combustion, the chemical reaction releases energy in the form of heat. This heat is a manifestation of the change in enthalpy during the combustion process.
2. Endothermic reactions: Some chemical reactions absorb heat from their surroundings, resulting in a decrease in temperature. These reactions have a positive ΔH, indicating an increase in enthalpy.
3. Phase transitions: When a substance changes its state, such as from a solid to a liquid or from a liquid to a gas, there is a change in enthalpy. This change is known as the heat of fusion or heat of vaporization, depending on the specific phase transition.

### Examples of Entropy

Here are a few examples that demonstrate the concept of entropy:

1. Mixing of gases: When two different gases are mixed together, the resulting system has a higher entropy compared to the separate individual gases. This is because the molecules are more randomly distributed in the mixed system.
2. Dissolution of a solid: When a solid substance dissolves in a liquid, the resulting solution has a higher entropy compared to the separate solid and liquid. The increased randomness of the dissolved particles contributes to the higher entropy.
3. Spreading of heat: If you have a hot cup of coffee and leave it in a room, the heat will spread from the hot coffee to the surrounding air. This spontaneous heat transfer occurs due to the tendency of the system to increase its entropy.

The examples above highlight how entropy is related to the randomness or disorder in a system. Processes that result in an increase in randomness or disorder tend to have a higher entropy.

### Enthalpy Formula

Enthalpy can be calculated using the following formula:

H = U + PV

In this formula, H represents enthalpy, U represents internal energy, P represents pressure, and V represents volume.

### Entropy Formula

Entropy can be calculated using the following formula:

S = Q/T

In this formula, S represents entropy, Q represents the heat transferred to or from a system, and T represents temperature.

These formulas allow for the quantification of enthalpy and entropy changes in various thermodynamic processes.

### Solved Examples on Difference Between Enthalpy and Entropy

Let’s solve a few examples to better understand the difference between enthalpy and entropy:

Example 1: A chemical reaction has a ΔH of -50 kJ and a ΔS of 100 J/K. Determine the ΔG at 25°C.

Solution: To calculate ΔG, we can use the formula:

ΔG = ΔH – TΔS

Given that ΔH = -50 kJ, ΔS = 100 J/K, and T = 25°C = 298 K, we can substitute these values into the formula:

ΔG = -50 kJ – (298 K)(100 J/K) = -50 kJ – 29.8 kJ = -79.8 kJ

Therefore, the ΔG for this reaction at 25°C is -79.8 kJ.

Example 2: A gas expands from a volume of 2 L to a volume of 4 L at a constant pressure of 1 atm. The temperature remains constant at 25°C. Calculate the change in entropy for this process.

Solution: To calculate the change in entropy, we can use the formula:

ΔS = nR ln(V2/V1)

Where ΔS represents the change in entropy, n represents the number of moles of gas, R represents the ideal gas constant, V1 represents the initial volume, and V2 represents the final volume.

In this case, the number of moles of gas (n) is constant, and the temperature remains constant. Therefore, we can simplify the formula to:

ΔS = R ln(V2/V1)

Given that R = 8.314 J/(mol·K), V1 = 2 L, and V2 = 4 L, we can substitute these values into the formula:

ΔS = (8.314 J/(mol·K)) ln(4/2) = (8.314 J/(mol·K)) ln(2) ≈ 5.76 J/K

Therefore, the change in entropy for this process is approximately 5.76 J/K.

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