Problem 153 - A Complete Resource Book in Chemistry for JEE Main

Question

In an irreversible process taking place at constant \(\mathrm{T}\) and \(\mathrm{P}\) and in which only pressure-volume work is being done, the change in Gibbs free energy \((\mathrm{dG})\) and change in entropy (dS), satisfy the criteria: [2003] (a) \((\mathrm{dS})_{\mathrm{V}, \mathrm{E}}<0,(\mathrm{dG})_{\mathrm{T}, \mathrm{P}}<0\) (b) \((\mathrm{dS})_{\mathrm{V} \mathbb{E}}>0,(\mathrm{dG})_{\mathrm{T}, \mathbb{P}}<0\) (c) \((\mathrm{dS})_{\mathrm{V}, \mathrm{E}}=0,(\mathrm{dG})_{\mathrm{T}, \mathrm{P}}=0\) (d) \((\mathrm{dS})_{\mathrm{VE}}=0,(\mathrm{dG})_{\mathrm{U}, \mathrm{p}}>0\)

Step-by-Step Solution

Answer

The correct answer is (b) \((dS)_{V, E}>0, (dG)_{T, P}<0\).

Step 1: Understanding Gibbs Energy Change in Irreversible Process

For an irreversible process occurring at constant temperature and pressure, the Gibbs free energy change \((dG)\) is less than zero, i.e., \((dG)_{T,P} < 0\), because such processes are spontaneous and decrease the Gibbs free energy on their own.

Step 2: Understanding Entropy Change in Irreversible Process

In any real (irreversible) process, the total entropy of the system and surroundings together increases, which means \((dS) > 0\) in the context of the universe. However, the problem asks for \((dS)_{V, E}\), and for an irreversible process, this is greater than zero.

Step 3: Matching Choices with Criteria

From the above understanding, spontaneous irreversible processes in constant T and P satisfy \((dS)_{V, E}>0, (dG)_{T, P}<0\). This matches option (b) in the problem statement.

Key Concepts

Irreversible Processes

An irreversible process is a natural and spontaneous phenomenon that cannot be reversed precisely to its original state without leaving changes in the surroundings. These processes proceed in one direction only and often result in an overall increase in entropy, distinguishing them from reversible processes where the system can be restored to its initial state with no net change in both the system and surroundings.

Real-world examples of irreversible processes include mixing of substances, natural diffusion across gradients, and spontaneous chemical reactions. Unlike reversible processes, these involve dissipative factors such as friction, turbulence, and heat loss. Since they can't perfectly reverse, they inherently result in a loss of usable energy, rendering them less efficient.

• Such processes occur naturally and spontaneously.
• They are accompanied by an increase in total entropy of the universe.
• Energy is usually lost to the surroundings in the form of heat.

Understanding the nature of irreversible processes helps in developing efficient methods to manage energy transitions and predict the spontaneity of chemical reactions.

Entropy Change

Entropy is a measure of disorder or randomness within a system. In the context of irreversible processes, the entropy changes illustrate how the randomness of a system evolves over time. For the universe, an irreversible process leads to an overall increase in entropy, making these processes vital for understanding thermodynamics.

Entropy change in an isolated system, specifically, is strictly positive during an irreversible process. This is summarized by the second law of thermodynamics, stating that the natural progression of time runs in the direction of increasing entropy in an isolated system.

• The change in entropy (dS) in the universe is greater than zero for irreversible processes.
• For systems at constant volume (V) and energy (E), \(dS_{V, E} > 0\) typifies the internal complexity changes during an irreversible process.
• Identifying when entropy changes can predict the directionality of processes.

The increase in entropy implies a degradation of useful energy, highlighting the importance of carefully considering entropy in systems design and energy management.

Spontaneity Criteria

The spontaneity criteria in thermodynamics relate to whether a process occurs naturally without outside intervention. In a system at constant temperature (T) and pressure (P), the change in Gibbs free energy \(dG_{T, P}\) determines the spontaneity. For a process to be spontaneous, Gibbs free energy should decrease (1d. This can be articulated mathematically as: if \(dG_{T, P} < 0\), the process is spontaneous.

This principle is particularly useful for predicting chemical reaction feasibility. In a chemical reaction or phase transition, if the Gibbs free energy decreases, the process proceeds without external force.

• Negative Gibbs free energy change implies spontaneity.
• Gibbs energy includes not only enthalpy but also entropy, providing a comprehensive criterion.
• Evaluating \(dG\) helps in understanding and anticipating the behavior of chemical reactions.

These criteria pave the way for sustainable energy practices by highlighting the conditions under which natural processes occur and can be harnessed.