Thermodynamics Notes

Introduction

Thermodynamics is a branch of physical chemistry that deals with the study of energy and its transformations. It is an essential topic for JEE Main Chemistry as it forms the foundation for understanding various physical and chemical processes. This study note will break down complex ideas into smaller, digestible sections, ensuring a comprehensive understanding of the topic.

Basic Concepts

System and Surroundings

• System: The part of the universe under study.
• Surroundings: Everything outside the system.
• Boundary: The real or imaginary surface that separates the system from its surroundings.

Types of Systems

1. Open System: Can exchange both energy and matter with surroundings.
2. Closed System: Can exchange only energy with surroundings, not matter.
3. Isolated System: Cannot exchange either energy or matter with surroundings.

State Functions and Path Functions

• State Functions: Properties that depend only on the state of the system (e.g., pressure $P$, volume $V$, temperature $T$, internal energy $U$).
• Path Functions: Properties that depend on the path taken to reach a particular state (e.g., work $W$, heat $q$).

First Law of Thermodynamics

Statement

The first law of thermodynamics states that energy can neither be created nor destroyed; it can only be transferred or transformed. Mathematically, it is represented as:

$$ \Delta U = q + W $$

Where:

• $\Delta U$ is the change in internal energy
• $q$ is the heat added to the system
• $W$ is the work done on the system

Sign Conventions

• $q > 0$: Heat is absorbed by the system (endothermic process).
• $q

< 0$: Heat is released by the system (exothermic process).

• $W >

0$: Work is done on the system.

• $W

< 0$: Work is done by the system.

Enthalpy

Definition

Enthalpy ($H$) is a state function defined as the sum of the internal energy ($U$) and the product of pressure ($P$) and volume ($V$):

$$ H = U + PV $$

Enthalpy Change

For processes at constant pressure, the change in enthalpy ($\Delta H$) is given by:

$$ \Delta H = \Delta U + P \Delta V $$

Second Law of Thermodynamics

Statement

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. It can remain constant for a reversible process but increases for an irreversible process.

Entropy

Entropy ($S$) is a measure of the disorder or randomness of a system. The change in entropy ($\Delta S$) for a process is given by:

$$ \Delta S = \frac{q_{\text{rev}}}{T} $$

Where $q_{\text{rev}}$ is the reversible heat exchange and $T$ is the absolute temperature.

Gibbs Free Energy

Definition

Gibbs free energy ($G$) is a state function that combines enthalpy and entropy to predict the spontaneity of a process:

$$ G = H - TS $$

Gibbs Free Energy Change

The change in Gibbs free energy ($\Delta G$) determines the spontaneity of a process:

• $\Delta G

< 0$: The process is spontaneous.

• $\Delta G >

0$: The process is non-spontaneous.

• $\Delta G = 0$: The system is in equilibrium.

Relationship with Equilibrium Constant

For a reaction at constant temperature and pressure, the change in Gibbs free energy is related to the equilibrium constant ($K$) by:

$$ \Delta G^\circ = -RT \ln K $$

Where:

• $R$ is the universal gas constant
• $T$ is the temperature in Kelvin
• $K$ is the equilibrium constant

Third Law of Thermodynamics

Statement

The third law of thermodynamics states that the entropy of a perfect crystal at absolute zero temperature is zero.

Conclusion

Thermodynamics is a fundamental topic in chemistry that provides insights into energy transformations and the spontaneity of processes. Understanding the laws of thermodynamics, along with concepts like enthalpy, entropy, and Gibbs free energy, is crucial for solving problems in JEE Main Chemistry.