Textbook Question
0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What are temperature T1?
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Ch 18: A Macroscopic Description of Matter
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 18, Problem 35a
A gas with an initial temperature of 900°C undergoes the process shown in FIGURE EX18.35. What type of process is this?
Verified step by step guidance1
Step 1: Analyze the graph provided. The graph shows pressure (p) on the y-axis and volume (V) on the x-axis. The curve represents the relationship between pressure and volume during the process. The curve is hyperbolic, indicating an inverse relationship between pressure and volume.
Step 2: Recognize the type of thermodynamic process. A hyperbolic curve on a p-V diagram typically represents an isothermal process, where the temperature remains constant throughout the process. This is because the product of pressure and volume (pV) remains constant, which is a characteristic of isothermal processes.
Step 3: Confirm the process type using the ideal gas law. The ideal gas law is given by . If temperature (T) is constant, then remains constant, which matches the behavior shown in the graph.
Step 4: Note that the initial temperature of the gas is given as 900°C. However, this temperature does not change during the process if it is isothermal. The temperature remains constant throughout the process.
Step 5: Conclude that the process shown in the graph is an isothermal process, based on the hyperbolic shape of the curve and the constant product of pressure and volume.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Ideal Gas Law
The Ideal Gas Law describes the relationship between pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas, expressed as PV = nRT. This law is fundamental in understanding gas behavior under various conditions and is crucial for analyzing processes involving gases, such as the one depicted in the graph.
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Ideal Gases and the Ideal Gas Law
Isothermal Process
An isothermal process occurs when a gas expands or compresses at a constant temperature. In the context of the graph, if the temperature remains constant while pressure and volume change, the process can be classified as isothermal, which is characterized by a hyperbolic curve on a pressure-volume graph.
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Thermodynamic Processes
Thermodynamic processes refer to the changes in state variables of a system, such as pressure, volume, and temperature. Understanding the type of process (isothermal, adiabatic, isobaric, or isochoric) is essential for analyzing how energy is transferred and transformed in a gas, as illustrated in the provided graph.
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Related Practice
Textbook Question
0.10 mol of argon gas is admitted to an evacuated 50 cm3 container at 20°C. The gas then undergoes an isochoric heating to a temperature of 300°C. Show the process on a pV diagram. Include a proper scale on both axes.
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Textbook Question
A gas with an initial temperature of 900°C undergoes the process shown in FIGURE EX18.35. How many moles of gas are there?
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Textbook Question
0.10 mol of argon gas is admitted to an evacuated 50 cm3 container at 20°C. The gas then undergoes an isochoric heating to a temperature of 300°C. What is the final pressure of the gas?
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Textbook Question
A 24-cm-diameter vertical cylinder is sealed at the top by a frictionless 20 kg piston. The piston is 84 cm above the bottom when the gas temperature is 303°C. The air above the piston is at 1.00 atm pressure. What will the height of the piston be if the temperature is lowered to 15°C?
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Textbook Question
0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What are pressure p2?
1643
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