Problem 24 - Chemistry: An Atoms-Focused Approach

Question

The 1996 Nobel Prize in Physics was awarded to Douglas Osheroff, Robert Richardson, and David Lee for discovering superfluidity (apparently frictionless flow) in \(^{3} \mathrm{He} .\) When \(^{3} \mathrm{He}\) is cooled to \(2.7 \mathrm{mK},\) the liquid settles into an ordered super fluid state. Predict the sign of the entropy change for the conversion of liquid \(^{3} \mathrm{He}\) into its super fluid state.

Step-by-Step Solution

Answer

Answer: The sign of the entropy change for the conversion is negative (\(ΔS < 0\)).

Step 1: (1. Understanding entropy and order)

(Entropy, denoted by 'S,' is a measure of disorder or randomness in a system. As a system becomes more ordered, its entropy decreases, while an increase in disorder will correspond to an increase in entropy. In general, the sign of the entropy change \(ΔS\) indicates whether the system is becoming more ordered (\(ΔS < 0\)) or more disordered (\(ΔS > 0\)).)

Step 2: (2. Identifying the change in order)

(According to the information given, liquid \(^{3}\mathrm{He}\) becomes an ordered superfluid at a temperature of 2.7 mK. From this, we infer that the transformation results in an increase in order within the system.)

Step 3: (3. Predicting the sign of entropy change)

(Since the transition from liquid \(^{3}\mathrm{He}\) to its superfluid state involves an increase in order, the entropy of the system will decrease. Therefore, the sign of the entropy change for the conversion is negative: \(ΔS < 0\).) So, the entropy change for the conversion of liquid \(^{3}\mathrm{He}\) into its superfluid state is negative, indicating an increase in order within the system.

Key Concepts

Entropy Change

Entropy is a concept from thermodynamics that helps us understand the level of disorder or randomness within a system. The more disordered the molecules in a system are, the higher the entropy. Conversely, as the system becomes more ordered, its entropy decreases. We use the symbol 'S' to denote entropy and calculate changes in entropy ( abla S) to determine whether a system has become more disordered or ordered.
When looking at a change of phase, like in the transition of liquid helium-3 (^{3} ext{He}) into its superfluid state, scientists examine the corresponding entropy change. If transitioning into a new state makes the system more structured and organized, the entropy decreases. This is represented by a negative change in entropy ( abla S < 0). In the specific case of liquid (^{3} ext{He}), as it forms a superfluid at very low temperatures (2.7 mK), it becomes extremely ordered. Thus, the transition accompanies a reduction in entropy, making the value negative.

Superfluidity

Superfluidity is a fascinating phase of matter where a fluid can flow without viscosity, or in layman's terms, without any resistance. This phenomenon occurs at extremely low temperatures. In the case of helium-3 ( (^{3} ext{He})), it turns into a superfluid upon cooling to about 2.7 millikelvin. At this point, the liquid achieves an unprecedented level of molecular order.

• In a superfluid state, helium-3 exhibits unique properties:
• It can flow through tiny pores without losing energy.
• The fluid climbs walls and defies gravity, in some cases.
• This behavior is due to the quantum mechanical effects that govern the particles at such low temperatures, leading to a coherent, ordered state.

Superfluidity isn't just a theoretical concept; it has practical implications and has been the focus of intense research since its discovery. Understanding superfluidity helps scientists grasp the underlying principles of quantum mechanics in macroscopic systems. The absence of viscosity allows for studies that unveil the unique behaviors of quantum particles in bulk.

Nobel Prize in Physics

The Nobel Prize in Physics is one of the most prestigious awards that an individual in the field can receive. In 1996, this honor went to Douglas Osheroff, Robert Richardson, and David Lee for their groundbreaking discovery of superfluidity in helium-3 ( (^{3} ext{He})). Their work unveiled a new phase of matter, showing how fluids can defy traditional laws of thermodynamics at extremely low temperatures.
This discovery wasn't just about superfluidity alone; it opened the door to understanding aspects of quantum mechanics and thermodynamics that were previously shrouded in mystery. It illustrated the complex nature of phase transitions in condensed matter physics and provided a vital platform for exploring quantum mechanics on a new level.

• Their pioneering research has helped develop further studies in areas like:
• Quantum computing, where understanding such states can lead to breakthroughs.
• Astrophysics, offering insights into behaviors of matter under extreme conditions.

Because of such contributions, these scientists exemplified how theoretical research can lead to discoveries that reshape our understanding of the physical world.