Textbook Question
What is the total rotational kinetic energy of 1.0 mol of nitrogen gas at 300 K?
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Ch 20: The Micro/Macro Connection
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 20, Problem 65b
A monatomic gas is adiabatically compressed to 1/8 of its initial volume. Does each of the following quantities change? If so, does it increase or decrease, and by what factor? If not, why not? The mean free path.
Verified step by step guidance1
Understand the concept of mean free path: The mean free path is the average distance a particle travels between collisions. It depends on the density of the gas and the cross-sectional area of the particles.
Recall that during adiabatic compression, the volume of the gas decreases, which increases the density of the gas. The density is inversely proportional to the volume, so if the volume is reduced to ⅛ of its initial value, the density increases by a factor of 8.
The mean free path is inversely proportional to the density of the gas. Since the density increases by a factor of 8, the mean free path decreases by the same factor.
Express the relationship mathematically: \( \lambda \propto \frac{1}{\rho} \), where \( \lambda \) is the mean free path and \( \rho \) is the density. If \( \rho \) increases by a factor of 8, \( \lambda \) decreases by a factor of 8.
Conclude that the mean free path decreases by a factor of 8 due to the increase in density caused by the adiabatic compression.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Mean Free Path
The mean free path is the average distance a particle travels between collisions with other particles. It is influenced by the density of the gas and the size of the particles. In a gas, as the volume decreases, the density increases, leading to more frequent collisions and a shorter mean free path.
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Mean Free Path
Adiabatic Process
An adiabatic process is one in which no heat is exchanged with the surroundings. In the case of a gas being compressed adiabatically, the work done on the gas increases its internal energy, which can lead to a rise in temperature. This process affects the behavior of the gas, including its pressure and volume, but not its heat content.
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Gas Density
Gas density is defined as the mass of gas per unit volume. When a gas is compressed to a smaller volume, its density increases. This increase in density directly affects the mean free path, as a higher density results in more frequent particle collisions, thereby reducing the average distance traveled between these collisions.
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Related Practice
Textbook Question
n moles of a diatomic gas with Cv = 5/2 R has initial pressure pi and volume Vi. The gas undergoes a process in which the pressure is directly proportional to the volume until the rms speed of the molecules has doubled. How much heat does this process require? Give your answer in terms of n, pi and Vi.
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Textbook Question
A water molecule has its three atoms arranged in a 'V' shape, so it has rotational kinetic energy around any of three mutually perpendicular axes. However, like diatomic molecules, its vibrational modes are not active at temperatures below 1000 K. What is the thermal energy of 2.0 mol of steam at a temperature of 160°C?
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Textbook Question
A nitrogen molecule consists of two nitrogen atoms separated by 0.11 nm, the bond length. Treat the molecule as a rotating dumbbell and find the rms angular velocity at this temperature of a nitrogen molecule around the z-axis, as shown in Figure 20.10.
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Textbook Question
The 2010 Nobel Prize in Physics was awarded for the discovery of graphene, a two-dimensional form of carbon in which the atoms form a two-dimensional crystal-lattice sheet only one atom thick. Predict the molar specific heat of graphene. Give your answer as a multiple of R.
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Textbook Question
A monatomic gas is adiabatically compressed to 1/8 of its initial volume. Does each of the following quantities change? If so, does it increase or decrease, and by what factor? If not, why not? The thermal energy of the gas.
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