Enthalpy Definition Derivation

Enthalpy Definition Derivation

May 03, 2023, 16:45 IST

Thermodynamics is the study of the relationships between heat, energy, and chemical reactions. It provides a fundamental understanding of the behavior of chemical systems and the transformations of energy in chemical reactions. Thermodynamic principles, such as enthalpy and entropy, are used to predict and optimize chemical reactions and processes.

Introduction

Enthalpy is a thermodynamic property that is commonly used in the study of chemical reactions and physical processes. It is a measure of the total energy of a system, including both its internal energy and the energy required to do work on the environment. In this article, we will provide an overview of enthalpy, its definition, derivation, and some frequently asked questions about this important concept.

Definition of Enthalpy

Enthalpy is defined as the sum of the internal energy (U) of a system and the product of pressure (P) and volume (V) of the system. Mathematically, it can be represented as:

H = U + PV

Where,

H = Enthalpy

U = Internal Energy

P = Pressure

V = Volume

Enthalpy is a state function, which means it depends only on the initial and final states of the system and not on the path taken to reach those states.

Derivation of Enthalpy

The derivation of enthalpy can be done by considering the first law of thermodynamics, which states that energy cannot be created or destroyed but can be transferred from one form to another. In other words, the change in internal energy (ΔU) of a system is equal to the heat (q) added to the system minus the work (w) done by the system.

dU = dQ - dW

where, dU is the change in internal energy, dQ is the heat added to the system, and dW is the work done by the system.

If the system is at constant pressure, the work done can be expressed as:

dW = -PdV

where, P is the pressure and dV is the change in volume.

Substituting this expression into the first law of thermodynamics gives:

dU = dQ + PdV

which is the same as the first law of thermodynamics. However, in this form, it is more convenient for studying systems at constant pressure.

If we integrate this equation between two states, we get:

ΔU = ΔQ + PΔV

Now, using the ideal gas law, we can express the change in specific volume as:

Δv = RΔT/P

where, R is the gas constant and ΔT is the change in temperature.

Substituting this expression into the previous equation gives:

Δu = Δq + RΔT

If we express the heat added per unit amount of substance in terms of the enthalpy change (ΔH), we get:

Δq = ΔH - PΔv

Substituting this expression into the previous equation gives:

Δu = ΔH - PΔv + RΔT

Rearranging the terms gives:

ΔH = Δu + PΔv - RΔT

Finally, substituting the definition of enthalpy (H = U + PV) into the above equation gives:

ΔH = ΔU + PΔV

OR

ΔH = ΔQ (at constant pressure)

This is the expression for the change in enthalpy at constant pressure, which is a useful quantity in thermodynamics.

Applications of Enthalpy

• Enthalpy change of a reaction - The enthalpy change of a chemical reaction is the difference between the enthalpies of the reactants and the products. It is a measure of the heat released or absorbed during a chemical reaction and is used to predict the feasibility and efficiency of chemical reactions.
• Heat transfer - It is used to calculate the amount of heat that is transferred during a process. This is important in many engineering applications, such as designing heating and cooling systems for buildings or industrial processes.
• Phase transitions - It is involved in the phase transitions of matter, such as melting and boiling. The enthalpy of fusion and vaporization are important properties in determining the amount of energy required to change the phase of a substance.
• Enthalpy of combustion - The enthalpy of combustion is the heat released when a substance is burned in the presence of oxygen. This property is important in determining the energy content of fuels and the efficiency of combustion engines.
• Thermodynamic cycles - Enthalpy is used in thermodynamic cycles, such as the Carnot cycle, which is a theoretical model for an ideal heat engine. These cycles are used to model the behavior of real-world systems and to improve their efficiency

Frequently Asked Questions (FAQs)

Q1. What is the significance of enthalpy in thermodynamics?

Ans. Enthalpy is a fundamental property in thermodynamics that describes the energy content of a system. It is a useful tool for studying physical and chemical systems and plays a crucial role in various fields of engineering and science.

Q2. What is the difference between internal energy and enthalpy?

Ans. Internal energy is the energy contained within a system, whereas enthalpy is the sum of internal energy and the product of pressure and volume. Enthalpy is a more useful quantity for studying systems at constant pressure.

Q3. Why is enthalpy a state function?

Ans. Enthalpy is a state function because its value depends only on the initial and final states of a system and not on the path taken between those states.

Q4. How is enthalpy related to heat?

Ans. Enthalpy is related to heat because, at constant pressure, the change in enthalpy is equal to the heat added to or removed from the system.