Problem 21 - A Complete Resource Book in Chemistry for JEE Main

Question

Identify the correct statement regarding entropy. (a) at absolute zero temperature, entropy of a perfectly crystalline substance is +ve. (b) at absolute zero temperature, entropy of a perfectly crystalline substance is taken to be zero (c) at absolute zero temperature, entropy of all crystalline substances in taken to be 0 . (d) at \(0^{\circ} \mathrm{C}\), entropy of a perfectly crystalline substance is taken to be 0 .

Step-by-Step Solution

Answer

The correct statement is (b): At absolute zero temperature, the entropy of a perfectly crystalline substance is taken to be zero.

Step 1: Understand the Concept of Entropy

Entropy is a measure of the disorder or randomness in a system. According to the third law of thermodynamics, the entropy of a perfectly crystalline substance approaches zero as the temperature approaches absolute zero, given that the crystal is in a perfect pattern with no defects.

Step 2: Analyze Each Statement

Go through each of the provided statements: - **Statement (a):** Claims entropy is positive at absolute zero, which conflicts with the third law of thermodynamics. - **Statement (b):** Aligns with the third law, as it states that entropy is zero at absolute zero for a perfect crystal. - **Statement (c):** Incorrect because not all substances are perfect crystals at absolute zero. - **Statement (d):** Incorrectly suggests zero entropy at 0°C, not absolute zero.

Step 3: Determine the Correct Statement

Based on the analysis: - Only statement (b) accurately reflects the third law of thermodynamics, which states that a perfectly crystalline substance has zero entropy at absolute zero temperature.

Key Concepts

Entropy

Entropy is a fundamental concept in thermodynamics that describes the level of disorder or randomness in a system. Imagine your room when it’s tidy versus when it’s messy. The messy room has higher entropy because things are scattered around and less ordered.
Just like your room, any system can have different degrees of disorder. Generally, the higher the entropy, the more unpredictable or chaotic the system is. In simple terms, an increase in entropy reflects an increase in disorder or dispersion.
Entropy is heavily influenced by temperature and phase changes. For example:

• When ice melts to water, there is an increase in entropy because water molecules are more disordered compared to ice.
• Heating a substance generally increases entropy as increasing temperature causes molecules to move more chaotically.

Understanding entropy helps in predicting how energy is distributed in physical systems and why certain processes, like a melting ice cube, happen spontaneously.

Absolute Zero

Absolute zero is the lowest temperature possible, characterized by zero Kelvin (0 K) or -273.15°C. It represents a point where the motion of particles that constitute matter theoretically comes to a complete stop. At this special temperature, the system’s entropy is minimized because particles are as ordered as they can possibly be.
The concept of absolute zero is crucial in the study of thermodynamics:

• At absolute zero, the entropy of a perfectly crystalline substance is zero, because the atoms are arranged in a perfect structure without any randomness.
• This implies no thermal energy remains in the object to produce randomness or movement.

Absolute zero is a theoretical limit that can never truly be reached due to the laws of physics. However, experiments and studies can approach these extremely low temperatures, providing valuable insights into the behavior of matter at near-zero conditions.

Perfectly Crystalline Substance

A perfectly crystalline substance is an idealized material whose internal structure is completely ordered. In such a substance, every atom is positioned precisely in a regular, repeating pattern throughout the entire crystal.
In reality, no crystal is perfectly crystalline, as imperfections like defects or impurities usually exist. However, for the purposes of scientific models and explanations, this perfect order is assumed.
The importance of perfect crystals lies in their relationship with entropy:

• At absolute zero, the entropy of these substances is considered zero, as there is no disarray among the atoms.
• This is a fundamental principle derived from the Third Law of Thermodynamics, asserting that entropy approaches zero as the temperature approaches absolute zero but only for perfect crystals.

Overall, the idea of a perfectly crystalline substance allows scientists to establish benchmarks and understand the limits of thermodynamic behaviors.