Problem 14 - A Complete Resource Book in Chemistry for JEE Main

Question

Considering entropy (S) as a thermodynamic parameter, the criterion for the spontaneity of any process is (a) \(\Delta \mathrm{S}_{\text {sytem }}+\Delta \mathrm{S}_{\text {sarouedimgs }}>0\) (b) \(\Delta \mathrm{S}_{\text {system }}-\Delta \mathrm{S}_{\text {samondings }}>0\) (c) \(\Delta \mathrm{S}_{\text {sytem }}>0\) (d) \(\Delta S_{\text {surmundings }}>0\)

Step-by-Step Solution

Answer

The criterion for spontaneity is (a) \( \Delta S_{\text{system}} + \Delta S_{\text{surroundings}} > 0 \).

Step 1: Understanding Spontaneity

In thermodynamics, a process is considered spontaneous if it occurs naturally without outside intervention. Spontaneity is related to the total entropy change, which includes both the system and its surroundings.

Step 2: Entropy Change Criterion

The key criterion for spontaneity in thermodynamics involves the total entropy change of the universe (system + surroundings). A process is spontaneous if the total entropy change is greater than zero.

Step 3: Analyzing Each Option

Let's analyze each given option:- (a) \( \Delta S_{\text{system}} + \Delta S_{\text{surroundings}} > 0 \): This states that the sum of the entropy changes of the system and its surroundings is positive, which aligns with the criterion for spontaneity.- (b) \( \Delta S_{\text{system}} - \Delta S_{\text{surroundings}} > 0 \): This would imply the system's entropy change is greater than the surroundings' decrease, which is not the same criterion for spontaneity.- (c) \( \Delta S_{\text{system}} > 0 \): This only considers the system's entropy, not the surroundings, which is incomplete.- (d) \( \Delta S_{\text{surroundings}} > 0 \): This only considers the surroundings' entropy, which is also incomplete.

Step 4: Selecting the Correct Option

Evaluating the given options against the criterion for spontaneity, option (a) \( \Delta S_{\text{system}} + \Delta S_{\text{surroundings}} > 0 \) is the correct condition for the spontaneity of a process because it considers the total entropy change.

Key Concepts

Spontaneity

In the world of thermodynamics, spontaneity refers to the tendency of a process to occur naturally, without any external force or energy input. The concept is analogous to the free flow of water downhill; naturally proceeding towards a state of less potential energy. A spontaneous process does not mean that it will happen quickly or instantaneously, it just means it has a natural inclination to occur over time.

A major player in determining spontaneity is entropy, which measures the level of disorder or randomness in a system. The driving force behind spontaneous processes is the increase in the total entropy of the universe. During such processes, the universe tends to its maximum disorder. It's crucial to remember that for a process to be truly spontaneous, the entropy change of both the system involved and its surroundings must be taken into account.

Thermodynamics

Thermodynamics is a branch of physics that deals with the relationships between heat, work, temperature, and energy in a system. It provides insights into how energy transitions between different forms and how this affects the matter involved.

The laws of thermodynamics underpin the understanding of processes in nature, including chemical reactions and phase changes. The first law focuses on the conservation of energy and dictates that energy can neither be created nor destroyed, only transformed. The second law, which incorporates the concept of entropy, suggests that energy transformations lead to an increase in disorder or randomness within a system and its surroundings. It's this second law that is pivotal to determining whether a process is spontaneous. Understanding these laws helps in predicting the direction in which a process will naturally proceed, guiding industries and scientific research in fields like chemistry and engineering.

Entropy Change Criterion

The entropy change criterion is fundamental in assessing the spontaneity of any thermodynamic process. This criterion states that for any spontaneous process, the total change in entropy, combining the effects on both the system and its surroundings, must be greater than zero:

\[ \Delta S_{\text{total}} = \Delta S_{\text{system}} + \Delta S_{\text{surroundings}} > 0 \]
This equation captures the essence of entropy's role in determining spontaneity. It emphasizes that both parts—the system and its surroundings—must contribute to the overall increase in disorder for the process to be considered spontaneous.

Let's look at an example: if a hot cup of coffee cools to room temperature, the decrease in entropy of the coffee (system) is less than the increase in entropy of the air (surroundings), resulting in a net positive change in entropy. Such insights offer a straightforward criterion to ascertain whether nature will favor a process, allowing scientists and engineers to make informed predictions and decisions in their work.