Book cover for College Physics Explore and Apply

College Physics Explore and Apply

Eugenia Etkina; Alan Van Heuvelen; Gorazd Planinši?

ISBN #9780134601823

2nd Edition

2,244 Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This section examines how irreversible processes constantly convert usable, organized energy into less useful, random, thermal energy, a transformation quantified by the concept of entropy. Through both microscopic (statistical counting of microstates) and macroscopic (heat transfer divided by temperature) approaches, entropy is shown to increase in spontaneous processes. These ideas underpin the second law of thermodynamics, which governs the operational limits of devices ranging from car engines to refrigerators. Additionally, the Carnot efficiency sets the theoretical ceiling for energy conversion efficiency in thermodynamic engines, highlighting the inherent energy losses in real-world systems.

Learning Objectives

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Key Concepts

CONCEPT

DEFINITION

Atomic Physics

The study of atomic models and structure, detailing the evolution from classical orbit models (e.g., Bohr’s model) to quantum mechanics with quantized energy levels, quantum numbers, the uncertainty principle, and tunneling.

Example Problems

Example 1

Types of energy and reversibility of a process Describe the types of energy that change, the work done on the system, and the energy transferred through heating during the following processes. Indicate whether a reverse process can occur. (a) Water at the top of Niagara Falls cascades onto the blades of an electric generator near the bottom of the falls, rotating the blades and generating an electric current that causes a lightbulb to glow. The water, generator, lightbulb, and Earth are the system. (b) Each second, your body converts 100 J of metabolic energy (converting complex molecules from food) to thermal energy transferred to the air surrounding your body. The system is your body and the surrounding air. (c) The hot gas in a cylinder pushes a piston, which causes the blades of an electric generator to turn, which in turn causes a lightbulb to glow briefly. The system is the original hot gas (which cools while pushing the piston), the generator, and the lightbulb (which first glows and then stops glowing and cools down).

Example 2

For the following processes, choose the initial and final states and describe the process using the physical quantities internal energy, work, and heating. Explain why the process is irreversible. (a) A large foam ball is moving vertically up at speed $v$ and reaches a maximum height $h^{\prime}$ somewhat less than $\sqrt{v^{2} / 2 g}$. The ball, Earth, and air are the system. (b) Two cups of water, one cold and the other hot, are mixed in an insulated bowl. The mixture reaches an intermediate temperature. The water in the cups is the system.

Example 3

Hourglass An hourglass starts with all of the sand in the top bulb. During the next hour, the sand slowly leaks into the bottom bulb. Describe the energy changes in a system that includes the glass, sand, and Earth. Is this a reversible or irreversible process? Explain.

Example 4

Car hits tree Your car slides on ice and runs into a tree, causing the front of the car to become slightly hotter and crumpled. The car and ice are the system. Indicate what object does the work on the system. Indicate whether heating occurs. Identify the types of energy that change. Are these quantities positive or negative? Explain.

Example 5

Human metabolism A 60-kg person consumes about 2000 kcal of food in one day. If $10 \%$ of this food energy is converted to thermal energy and cannot leave the body, estimate the temperature change of the person. Note: $1 \mathrm{kcal}=4180 \mathrm{J} .$ Is this a reversible or irreversible process?
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Step-by-Step Explanations

QUESTION

How does a waterfall demonstrate an irreversible process in terms of energy conversion?\nStep-by-step Answer:\nStep 1: Identify the initial state where water at the top of a waterfall has high gravitational potential energy (organized energy).\nStep 2: As water falls, gravitational energy is converted into kinetic energy and then into internal thermal energy upon impact.\nStep 3: Recognize that the reverse process (thermal energy spontaneously converting back into organized gravitational energy to cause water ascent) does not occur naturally.\nFinal Answer: The waterfall is irreversible because the conversion from organized gravitational potential energy into random thermal energy cannot spontaneously reverse.\n\n- Topic: Statistical Definition of Entropy \nQuestion: Using the equation S = kB ln(Vi), how is the entropy of a macrostate determined for a system of atoms?\nStep-by-step Answer:\nStep 1: Count the number of microstates (Vi) corresponding to the given macrostate using combinatorial logic (e.g., Eq. (16.1) for atoms divided between two halves of a container).\nStep 2: Apply the equation S = kB ln(Vi), where kB is Boltzmann\u2019s constant, to obtain the entropy.\nStep 3: Understand that a higher count (Vi) indicates a more disordered state with greater entropy.\nFinal Answer: The entropy is directly related to the logarithm of the number of microstates, quantifying disorder.\n\n- Topic: Thermodynamic Engine Efficiency \nQuestion: How do you calculate the efficiency of a thermodynamic engine from the energy transfers during a cycle?\nStep-by-step Answer:\nStep 1: Identify the energy transferred from the hot reservoir QH to the working substance and the energy exhausted to the cold reservoir QC.\nStep 2: Use the work done by the engine W = QH - QC, as the net work output.\nStep 3: Calculate efficiency using the definition e = W / QH.\nFinal Answer: The efficiency is the ratio of the net work done by the engine to the energy input from the hot reservoir.\n\n"

STEP-BY-STEP ANSWER:

Step 1: Identify the initial state where water at the top of a waterfall has high gravitational potential energy (organized energy).\nStep 2: As water falls, gravitational energy is converted into kinetic energy and then into internal thermal energy upon impact.\nStep 3: Recognize that the reverse process (thermal energy spontaneously converting back into organized gravitational energy to cause water ascent) does not occur naturally.\nFinal Answer: The waterfall is irreversible because the conversion from organized gravitational potential energy into random thermal energy cannot spontaneously reverse.\n\n- Topic: Statistical Definition of Entropy \nQuestion: Using the equation S = kB ln(Vi), how is the entropy of a macrostate determined for a system of atoms?\nStep-by-step Answer:\nStep 1: Count the number of microstates (Vi) corresponding to the given macrostate using combinatorial logic (e.g., Eq. (16.1) for atoms divided between two halves of a container).\nStep 2: Apply the equation S = kB ln(Vi), where kB is Boltzmann\u2019s constant, to obtain the entropy.\nStep 3: Understand that a higher count (Vi) indicates a more disordered state with greater entropy.\nFinal Answer: The entropy is directly related to the logarithm of the number of microstates, quantifying disorder.\n\n- Topic: Thermodynamic Engine Efficiency \nQuestion: How do you calculate the efficiency of a thermodynamic engine from the energy transfers during a cycle?\nStep-by-step Answer:\nStep 1: Identify the energy transferred from the hot reservoir QH to the working substance and the energy exhausted to the cold reservoir QC.\nStep 2: Use the work done by the engine W = QH - QC, as the net work output.\nStep 3: Calculate efficiency using the definition e = W / QH.\nFinal Answer: The efficiency is the ratio of the net work done by the engine to the energy input from the hot reservoir.\n\n"
Final Answer: The waterfall is irreversible because the conversion from organized gravitational potential energy into random thermal energy cannot spontaneously reverse.\n\n- Topic: Statistical Definition of Entropy \nQuestion: Using the equation S = kB ln(Vi), how is the entropy of a macrostate determined for a system of atoms?\nStep-by-step Answer:\nStep 1: Count the number of microstates (Vi) corresponding to the given macrostate using combinatorial logic (e.g., Eq. (16.1) for atoms divided between two halves of a container).\nStep 2: Apply the equation S = kB ln(Vi), where kB is Boltzmann\u2019s constant, to obtain the entropy.\nStep 3: Understand that a higher count (Vi) indicates a more disordered state with greater entropy.\nFinal Answer: The entropy is directly related to the logarithm of the number of microstates, quantifying disorder.\n\n- Topic: Thermodynamic Engine Efficiency \nQuestion: How do you calculate the efficiency of a thermodynamic engine from the energy transfers during a cycle?\nStep-by-step Answer:\nStep 1: Identify the energy transferred from the hot reservoir QH to the working substance and the energy exhausted to the cold reservoir QC.\nStep 2: Use the work done by the engine W = QH - QC, as the net work output.\nStep 3: Calculate efficiency using the definition e = W / QH.\nFinal Answer: The efficiency is the ratio of the net work done by the engine to the energy input from the hot reservoir.\n\n"

"- Topic: Waterfall as an Irreversible Process \nQuestion: How does a waterfall demonstrate an irreversible process in terms of energy conversion?\nStep-by-step Answer:\nStep 1: Identify the initial state where water at the top of a waterfall has high gravitational potential energy (organized energy).\nStep 2: As water falls, gravitational energy is converted into kinetic energy and then into internal thermal energy upon impact.\nStep 3: Recognize that the reverse process (thermal energy spontaneously converting back into organized gravitational energy to cause water ascent) does not occur naturally.\nFinal Answer: The waterfall is irreversible because the conversion from organized gravitational potential energy into random thermal energy cannot spontaneously reverse.\n\n- Topic: Statistical Definition of Entropy \nQuestion: Using the equation S = kB ln(Vi), how is the entropy of a macrostate determined for a system of atoms?\nStep-by-step Answer:\nStep 1: Count the number of microstates (Vi) corresponding to the given macrostate using combinatorial logic (e.g., Eq. (16.1) for atoms divided between two halves of a container).\nStep 2: Apply the equation S = kB ln(Vi), where kB is Boltzmann\u2019s constant, to obtain the entropy.\nStep 3: Understand that a higher count (Vi) indicates a more disordered state with greater entropy.\nFinal Answer: The entropy is directly related to the logarithm of the number of microstates, quantifying disorder.\n\n- Topic: Thermodynamic Engine Efficiency \nQuestion: How do you calculate the efficiency of a thermodynamic engine from the energy transfers during a cycle?\nStep-by-step Answer:\nStep 1: Identify the energy transferred from the hot reservoir QH to the working substance and the energy exhausted to the cold reservoir QC.\nStep 2: Use the work done by the engine W = QH - QC, as the net work output.\nStep 3: Calculate efficiency using the definition e = W / QH.\nFinal Answer: The efficiency is the ratio of the net work done by the engine to the energy input from the hot reservoir.\n\n"

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