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Mobile App Chapter 20: Problem 14
Predict the sign of \(\Delta S_{\text {sys }}\) for each process: (a) Alcohol evaporates. (b) A solid explosive converts to a gas. (c) Perfume vapors diffuse through a room.
Short Answer
Expert verified
(a) Positive, (b) Positive, (c) Positive.
Step by step solution
01
Identify \(\text{process}\text \)
Determine the type of process happening in each scenario by analyzing the phase change or diffusion.
02
Title - Determine the Entropy Change
Predict the sign of the entropy change, \(\text{\Delta S }_{\text {sys }}\), based on the nature of the process.
03
Title - Evaluate each scenario individually
Evaluate the change in entropy for each given scenario.
04
Scenario (a)
Alcohol evaporates. Evaporation is a phase change from liquid to gas, which increases disorder. Thus, \(\text{\Delta S }_{\text {sys }} \) is positive.
05
Scenario (b)
A solid explosive converts to a gas. This is a phase change from solid-to-gas, which significantly increases disorder. \(\text{\Delta S }_{\text {sys }} \) is positive.
06
Scenario (c)
Perfume vapors diffuse through a room. Diffusion leads to more disorder or randomness as the vapors spread out. Thus, \(\text{\Delta S }_{\text {sys }} \) is positive.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Phase Change
A phase change refers to the transformation of a substance from one state of matter to another, such as from solid to liquid, liquid to gas, or solid to gas. Each phase change involves energy exchange and reorganization of particles. For example, when alcohol evaporates, it changes from a liquid to a gas. This requires energy to overcome the intermolecular forces holding the liquid together, leading to an increase in the system's disorder. As particles move from a more ordered liquid state to a more disordered gas state, the entropy \(\Delta S_\text{sys}\) increases.
Entropy
Entropy is a measure of the disorder or randomness in a system. It quantifies the number of ways particles can be arranged while still maintaining the same total energy. In thermodynamics, processes that increase disorder lead to a positive change in entropy. For instance, when a solid explosive converts to a gas, the particles move from a rigid, ordered state to a highly dispersed, random state. This significant increase in disorder results in a positive \(\Delta S_\text{sys}\). Entropy changes can help predict the direction of spontaneous processes.
Diffusion
Diffusion is the process by which particles spread out from an area of high concentration to an area of low concentration until they are evenly distributed. This occurs naturally and increases the system's disorder. For example, when perfume vapors diffuse through a room, the volatile molecules spread out and mix with the air. Initially confined to a small region, these molecules gradually disperse, increasing randomness and resulting in a positive change in entropy, \(\Delta S_\text{sys}\).
Disorder
Disorder in a physical context refers to the randomness or lack of structure in a system. Higher disorder means higher entropy. Processes that increase disorder, such as phase changes from solid or liquid to gas, or diffusion, generally result in a positive change in entropy. When evaluating scenarios like a solid explosive converting to gas or alcohol evaporating, one can predict an increase in disorder. Thus, these transformations lead to a positive \(\Delta S_\text{sys}\). Understanding disorder is crucial for predicting the behavior of various physical and chemical processes.
Chemical Processes
Chemical processes involve reactions and transformations that can alter the state of a material and its entropy. When analyzing these processes, it's essential to consider the direction and extent of the change in disorder. For example, in a solid explosive conversion, the reactant phase (solid) changes to the product phase (gas). This phase transition indicates a significant increase in entropy due to the dispersal of molecules. Each chemical process can be evaluated for its changes in entropy, helping predict whether the reactions proceed spontaneously based on the increase in disorder.
