Understanding the Decrease of Entropy When Heat is Extracted: A Case Analysis During Phase Changes

In thermodynamics, the concept of entropy is a critical factor in understanding the behavior of various systems. This article will delve into the intriguing scenario where the entropy of a system decreases when heat is extracted at a constant temperature. We will explore this phenomenon through practical examples, such as a substance undergoing a phase change, and provide a detailed explanation of the underlying principles.

The Concept of Entropy

Entropy, denoted by the symbol S, is a measure of the possible number of microscopic configurations of a macroscopic system in equilibrium. It is a fundamental quantity in thermodynamics and statistical mechanics, providing a criterion for the direction of spontaneous processes. According to the second law of thermodynamics, the total entropy of an isolated system can never decrease over time.

Phase Changes and Entropy

One classic example that showcases the decrease in entropy when heat is extracted is a phase change, such as freezing. Consider a test tube of water placed in an ethanol bath just below the freezing point of water. As the water begins to freeze, heat is extracted from the system, but the temperature remains constant. During this process, the water transforms into ice, and the entropy of the system decreases.

This phenomenon can be explained using the following equation for the change in free energy at constant temperature:

Change in Free Energy at Constant Temperature

The change in free energy (G) at constant temperature can be expressed as:

G H - TS

Where:

H is the enthalpy of the system T is the absolute temperature S is the entropy of the system

The entropy change (ΔS) can be derived as:

ΔS H - G / T

In the context of heat extraction, if heat is taken out of the system (H

Entropy and Entropy Change in Practical Scenarios

When heat is taken out of a system at a constant temperature, the entropy of the system decreases, as defined by the equation dS ΔQ / T. If negative heat input (ΔQ

However, the total entropy of the universe must still increase. This is because the heat that has been extracted must flow to a colder region (T_C), where it increases the entropy of that region. Thus, the overall entropy of the universe increases, satisfying the second law of thermodynamics.

Special Cases and Contrived Systems

It is important to note that under certain conditions, entropy can decrease when heat is added. This is a special case where the system has a negative temperature. In such systems, the addition of heat leads to a decrease in entropy. These contrived systems are fascinating and go against the typical understanding of entropy behavior.

Conclusion

During phase changes, such as freezing, the entropy of a system can decrease when heat is extracted at a constant temperature. This phenomenon is explained through the principles of thermodynamics and entropy, which dictate that the total entropy of the universe must always increase. Understanding these concepts is crucial for a deeper comprehension of the behavior of various physical systems.

References

N. Thermodynamics and Statistical Mechanics by P.V. Panat, late Ex CSIR Emeritus Professor, Physics Department, University of Pune, Pune, India (Indian Edition) - Cheaper than a good lunch in an A/C hotel in Pune city. Note that the Indian edition may contain typographical errors, but the foreign edition is available and may be error-free.