Textbook Question
Imagine that you are climbing a mountain. Which of the following are state functions? b. The change in elevation during the climb
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Ch.5 - Thermochemistry
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970
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Table of contents
- Ch.1 - Introduction: Matter, Energy, and Measurement111
- Ch.2 - Atoms, Molecules, and Ions166
- Ch.3 - Chemical Reactions and Reaction Stoichiometry138
- Ch.4 - Reactions in Aqueous Solution127
- Ch.5 - Thermochemistry104
- Ch.6 - Electronic Structure of Atoms109
- Ch.7 - Periodic Properties of the Elements107
- Ch.8 - Basic Concepts of Chemical Bonding102
- Ch.9 - Molecular Geometry and Bonding Theories120
- Ch.10 - Gases122
- Ch.11 - Liquids and Intermolecular Forces79
- Ch.12 - Solids and Modern Materials102
- Ch.13 - Properties of Solutions99
- Ch.14 - Chemical Kinetics153
- Ch.15 - Chemical Equilibrium83
- Ch.16 - Acid-Base Equilibria109
- Ch.17 - Additional Aspects of Aqueous Equilibria117
- Ch.18 - Chemistry of the Environment60
- Ch.19 - Chemical Thermodynamics109
- Ch.20 - Electrochemistry113
- Ch.21 - Nuclear Chemistry79
- Ch.22 - Chemistry of the Nonmetals52
- Ch.23 - Transition Metals and Coordination Chemistry57
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry7
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook
Chapter 5, Problem 25b
A gas is confined to a cylinder fitted with a piston and an electrical heater, as shown here:
Suppose that current is supplied to the heater so that 100 J of energy is added. Consider two different situations. In case (1) the piston is allowed to move as the energy is added. In case (2) the piston is fixed so that it cannot move. (b) Identify the sign (positive, negative, or zero) of q and w in each case?
Verified step by step guidance1
Identify the system and surroundings: The gas inside the cylinder is the system, and everything outside the cylinder is the surroundings.
Understand the first law of thermodynamics: ΔU = q + w, where ΔU is the change in internal energy, q is the heat added to the system, and w is the work done by the system.
Analyze case (1) where the piston is allowed to move: When energy is added, the gas expands, doing work on the surroundings. Here, q is positive (since heat is added to the system), and w is negative (since the system does work on the surroundings).
Analyze case (2) where the piston is fixed: When energy is added, the volume does not change, so no work is done. Here, q is positive (since heat is added to the system), and w is zero (since no work is done).
Summarize the signs: In case (1), q is positive and w is negative. In case (2), q is positive and w is zero.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
First Law of Thermodynamics
The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. In the context of the gas in the cylinder, the energy added as heat (q) can either increase the internal energy of the gas or do work (w) on the piston, depending on whether the piston is allowed to move.
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01:18
First Law of Thermodynamics
Heat (q) and Work (w)
In thermodynamics, heat (q) refers to the energy transferred due to temperature differences, while work (w) is the energy transferred when a force is applied over a distance. In the scenarios presented, the movement of the piston affects how energy is distributed between heat and work, influencing their signs based on the system's constraints.
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00:44Heat Capacity
System Constraints
The constraints of a system, such as whether the piston can move or is fixed, significantly impact the thermodynamic processes occurring. In case (1), the piston moves, allowing the gas to do work on the surroundings, while in case (2), the fixed piston means no work is done, affecting the signs of q and w differently in each scenario.
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02:06Entropy of the System
Related Practice
Textbook Question
Imagine that you are climbing a mountain. Which of the following are state functions? a. The distance you walk during your climb to the top
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Textbook Question
Consider a system consisting of two oppositely charged spheres hanging by strings and separated by a distance r1, as shown in the accompanying illustration. Suppose they are separated to a larger distance r2, by moving them apart. (a) What change, if any, has occurred in the potential energy of the system?
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Textbook Question
Calculate ΔE and determine whether the process is endothermic or exothermic for the following cases: (a) q = 0.763 kJ and w = -840 J.
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Textbook Question
A gas is confined to a cylinder fitted with a piston and an electrical heater, as shown here:
Suppose that current is supplied to the heater so that 100 J of energy is added. Consider two different situations. In case (1) the piston is allowed to move as the energy is added. In case (2) the piston is fixed so that it cannot move. (a) In which case does the gas have the higher temperature after addition of the electrical energy?
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