Textbook Question
A cylinder contains nitrogen gas. A piston compresses the gas to half its initial volume. Afterward, has the mass density of the gas changed? If so, by what factor? If not, why not?
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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 21a
A gas at 100°C fills volume V0. If the pressure is held constant, what is the volume if the Celsius temperature is doubled?
Verified step by step guidance1
Understand the relationship between temperature and volume for a gas at constant pressure. This is described by Charles's Law, which states that \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \), where \( V \) is the volume and \( T \) is the absolute temperature in Kelvin.
Convert the initial temperature from Celsius to Kelvin. The formula for conversion is \( T(K) = T(°C) + 273.15 \). For \( T_1 = 100°C \), calculate \( T_1(K) = 100 + 273.15 \).
Double the Celsius temperature as stated in the problem. If the initial temperature is \( 100°C \), the new Celsius temperature is \( 2 \times 100 = 200°C \). Convert this to Kelvin: \( T_2(K) = 200 + 273.15 \).
Use Charles's Law to find the new volume \( V_2 \). Rearrange the equation to solve for \( V_2 \): \( V_2 = V_1 \times \frac{T_2}{T_1} \). Substitute \( T_1 \) and \( T_2 \) in Kelvin into the equation.
Simplify the expression to determine the proportional change in volume. Since \( T_2 \) is double \( T_1 \), \( V_2 \) will also be double \( V_1 \). Thus, \( V_2 = 2 \times V_1 \).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Charles's Law
Charles's Law states that the volume of a gas is directly proportional to its absolute temperature (in Kelvin) when pressure is held constant. This means that if the temperature increases, the volume will also increase, and vice versa. The relationship can be expressed mathematically as V1/T1 = V2/T2, where V is volume and T is temperature.
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10:20
Gauss' Law
Absolute Temperature
Absolute temperature is measured in Kelvin and is crucial for gas law calculations. It is obtained by adding 273.15 to the Celsius temperature. For example, 100°C corresponds to 373.15 K. Using absolute temperature ensures that the proportional relationships in gas laws are valid, as negative temperatures in Celsius do not make physical sense in this context.
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04:54Introduction To Temperature Scales
Volume-Temperature Relationship
The volume-temperature relationship in gases indicates that if the temperature of a gas is doubled (in Kelvin), the volume will also double, provided the pressure remains constant. This principle allows us to predict how changes in temperature affect the volume of a gas, which is essential for solving problems involving gas behavior under varying thermal conditions.
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05:21Volume Thermal Expansion
Related Practice
Textbook Question
A gas at 100°C fills volume V₀. If the pressure is held constant, what is the volume if the Kelvin temperature is doubled?
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Textbook Question
The total lung capacity of a typical adult is 5.0 L. Approximately 20% of the air is oxygen. At sea level and at a body temperature of 37°C, how many oxygen molecules do the lungs contain at the end of a strong inhalation?
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Textbook Question
A surveyor has a steel measuring tape that is calibrated to be 100.000 m long (i.e., accurate to ±1 mm) at 20°C. If she measures the distance between two stakes to be 65.175 m on a 3°C day, does she need to add or subtract a correction factor to get the true distance? How large, in mm, is the correction factor?
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Textbook Question
Common outdoor thermometers are filled with red-colored ethyl alcohol. One thermometer has a 0.40-mm-diameter capillary tube attached to a 9.0-mm-diameter spherical bulb. On a 0°C morning, the column of alcohol stands 30 mm above the bulb. What is the temperature in °C when the column of alcohol stands 130 mm above the bulb? The expansion of the glass is much less than that of the alcohol and can be ignored.
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Textbook Question
The solar corona is a very hot atmosphere surrounding the visible surface of the sun. X-ray emissions from the corona show that its temperature is about 2×106 K. The gas pressure in the corona is about 0.03 Pa. Estimate the number density of particles in the solar corona.
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