Question

For the process $$ \mathrm{H}_{2} \mathrm{O}(I) \rightarrow \mathrm{H}_{2} \mathrm{O}(g) $$ at \(T=100^{\circ} \mathrm{C}\) and 1 atmosphere pressure, the correct choice is (A) \(\Delta \mathrm{S}_{\text {system }}>0\) and \(\Delta \mathrm{S}_{\text {surroundings }}>0\) (B) \(\Delta \mathrm{S}_{\text {system }}>0\) and \(\Delta \mathrm{S}_{\text {surroundings }}<0\) (C) \(\Delta \mathrm{S}_{\text {system }}<0\) and \(\Delta \mathrm{S}_{\text {surroundings }}>0\) (D) \(\Delta \mathrm{S}_{\text {system }}<0\) and \(\Delta \mathrm{S}_{\text {surroundings }}<0\)

Short answer

\(\Delta S_{\text{system}} > 0\) and \(\Delta S_{\text{surroundings}} < 0\), so the correct choice is (B).

Step-by-step solution

Understand the System

The process described is the phase change of water from liquid to gas (boiling) at the boiling point temperature of water, which is 100 degrees Celsius at 1 atmosphere pressure.

Determine the Entropy Change of the System

During the phase transition from liquid to gas, the entropy of the system increases because the molecules in the gaseous state are more disordered compared to the liquid state. Therefore, \(\Delta S_{\text{system}} > 0\).

Decide the Entropy Change of the Surroundings

Since the system is at constant temperature and pressure, the heat transfer is a reversible process. The surroundings lose heat to the system as it gains enough energy to transition from liquid to gas, thereby decreasing the entropy of the surroundings. Thus, \(\Delta S_{\text{surroundings}} < 0\).

Key concepts

Thermodynamics

Thermodynamics is a fundamental branch of physics that deals with the principles governing heat and energy and their ability to perform work. At the core of thermodynamics are four laws that define how energy can be transferred and converted within a system.

When examining processes like the boiling of water, thermodynamics helps us understand the flow of heat and the work done by the system. In the phase transition described, heat is absorbed by the water to transform from liquid to gas, a process which is described by the first law of thermodynamics—conservation of energy.

Thermodynamics also includes the concept of entropy, which can be seen as a measure of disorder in a system. This measure plays a crucial role during phase changes. Knowledge of thermodynamics is essential for students preparing for exams like the JEE Advanced in physics, where understanding how to apply these principles in practical scenarios is key.

Phase Change

A phase change is the transition of matter from one state—solid, liquid, or gas—to another. Common phases transformations include melting, freezing, boiling, and condensing. Each of these processes involves a change in the energy of a system, typically in the form of heat transfer.

When water boils, it undergoes a phase change from liquid to gas at a specific temperature and pressure. This requires heat, known in thermodynamics as the latent heat of vaporization. During a phase change, the temperature of the system remains constant even though heat is being added, because the energy is used to break intermolecular bonds rather than increasing kinetic energy.

Though it might seem counterintuitive, understanding how the temperature remains constant during the phase change is key for problems involving thermodynamic processes on exams like JEE Advanced physics.

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it's a central concept that quantifies the number of ways a system can be arranged, often associated with the second law of thermodynamics, which states that the total entropy of an isolated system can never decrease over time.

During phase transitions, such as boiling water, entropy plays a critical role. The transition from liquid to gas increases the disorder among water molecules, as they spread out and move more freely in the gaseous state, leading to an increase in entropy (). It's important for students to grasp this concept deeply, as entropy can be a challenging topic that is frequently tested in exams like the JEE Advanced physics section.

Understanding entropy also helps to comprehend the direction in which natural processes occur, since they tend to move towards a state of higher entropy or disorder.

JEE Advanced Physics

The JEE Advanced exam is one of the most competitive entrance exams for engineering aspirants in India. Physics is a substantial part of this assessment, requiring a comprehensive understanding of various concepts including mechanics, electromagnetism, thermodynamics, and modern physics.

In regards to thermodynamics and phase transitions, JEE Advanced physics questions often involve calculations and conceptual understanding of entropy, heat transfer, and phase changes. The exam tests the application of theoretical knowledge through problems that mimic real-world scenarios.

To excel in the thermodynamics section of JEE Advanced physics, it's critical for students to master problem-solving techniques and deeply understand concepts like entropy change during phase transitions. Exercises that challenge students to deduce the entropy changes in both the system and surroundings, similar to the given textbook problem on the phase change of water, are excellent practice for this prestigious exam.