The accompanying diagram shows how entropy varies with temperature for a substance that is a gas at the highest temperature shown. (c) If this substance is a perfect crystal at T = 0 K, what is the value of S at this temperature?

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Identify the concept of entropy (S) and its relation to temperature. Entropy is a measure of the disorder or randomness in a system.

Recall the Third Law of Thermodynamics, which states that the entropy of a perfect crystal at absolute zero (0 K) is exactly zero.

Understand that a perfect crystal is a substance with a perfectly ordered structure, meaning there is only one possible microstate.

Apply the Third Law to the given problem: since the substance is a perfect crystal at T = 0 K, the entropy S at this temperature is zero.

Conclude that the value of S at T = 0 K for a perfect crystal is 0 J/K.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the number of microscopic configurations that correspond to a thermodynamic system's macroscopic state. Higher entropy indicates greater disorder, while lower entropy suggests more order. Understanding entropy is crucial for analyzing the behavior of substances at different temperatures.

Third Law of Thermodynamics

The Third Law of Thermodynamics states that as the temperature of a perfect crystal approaches absolute zero (0 K), the entropy of the crystal approaches a constant minimum, which is typically zero. This principle implies that at absolute zero, a perfect crystal has no disorder, and thus its entropy is zero. This law is fundamental in understanding the behavior of materials at low temperatures.

Temperature and Phase Changes

Temperature is a measure of the average kinetic energy of the particles in a substance. As temperature changes, substances can undergo phase changes, affecting their entropy. For gases, the entropy increases significantly with temperature due to increased molecular motion and disorder. Recognizing how temperature influences entropy is essential for interpreting thermodynamic diagrams and understanding the state of a substance.

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Entropy in Phase Changes

Related Practice

Textbook Question

b. If energy can flow in and out of the system to maintain a constant temperature during the process, what can you say about the entropy change of the surroundings as a result of this process?

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Textbook Question

Predict the signs of ΔH and ΔS for this reaction. Explain your choice.

Textbook Question

Isomers are molecules that have the same chemical formula but different arrangements of atoms, as shown here for two isomers of pentane, C₅H₁₂.

(a) Do you expect a significant difference in the enthalpy of combustion of the two isomers? Explain.

Textbook Question

Isomers are molecules that have the same chemical formula but different arrangements of atoms, as shown here for two isomers of pentane, C₅H₁₂.

(b) Which isomer do you expect to have the higher standard molar entropy? Explain.