Textbook Question
A 20-cm-diameter cylinder that is 40 cm long contains 50 g of oxygen gas at 20°C. What is the reading of a pressure gauge attached to the tank?
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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 28a
A gas with initial state variables p1, V1, and T1 expands isothermally until V2 = 2V1. What are T1?
Verified step by step guidance1
Step 1: Recognize that the process is isothermal, meaning the temperature remains constant throughout the expansion. Therefore, T₁ = T₂.
Step 2: Recall the ideal gas law, which is expressed as , where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.
Step 3: Since the temperature is constant (T₁ = T₂), the product of pressure and volume remains constant during the expansion. This is expressed as .
Step 4: Substitute the given relationship for the final volume, , into the equation to find the relationship between p₁ and p₂.
Step 5: Conclude that since the temperature remains constant, T₂ = T₁. No further calculation is needed for T₂.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Isothermal Process
An isothermal process is a thermodynamic process in which the temperature of the system remains constant. For an ideal gas, this means that any heat added to the system is used to do work, rather than increasing the internal energy. In this scenario, since the gas expands isothermally, the temperature T₂ will equal the initial temperature T₁.
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Entropy & Ideal Gas Processes
Ideal Gas Law
The Ideal Gas Law is a fundamental equation in thermodynamics that relates the pressure, volume, temperature, and number of moles of an ideal gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. This law helps in understanding how changes in volume and temperature affect the state of the gas during the isothermal expansion.
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Charles's Law
Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is held constant. This relationship implies that if the volume of a gas increases, its temperature must also increase, provided the pressure does not change. In the context of the isothermal expansion, while the volume doubles, the temperature remains constant, reinforcing the concept that T₂ = T₁.
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Related Practice
Textbook Question
A gas with initial state variables p1, V1, and T1 expands isothermally until V2 = 2V1. What are p2?
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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?
1873
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Textbook Question
A 20-cm-diameter cylinder that is 40 cm long contains 50 g of oxygen gas at 20°C. What is the number density of the oxygen?
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1
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Textbook Question
A gas with initial state variables p1, V1, and T1 is cooled in an isochoric process until p2 = (1/3)p1. What are V2?
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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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