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?
1
views
Ch 18: A Macroscopic Description of Matter
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
Not the one you use?Change textbookSelect a different textbook
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 23
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?
Verified step by step guidance1
Step 1: Begin by identifying the key variables in the problem. The total lung capacity is 5.0 L, and 20% of the air is oxygen. The temperature is given as 37°C, which needs to be converted to Kelvin using the formula: \( T(K) = T(°C) + 273.15 \).
Step 2: Use the ideal gas law \( PV = nRT \) to relate the volume, pressure, and temperature to the number of moles of gas. Assume the pressure \( P \) is 1 atm (sea level pressure), \( V \) is 5.0 L, \( R \) is the ideal gas constant \( 0.0821 \, \text{L·atm/(mol·K)} \), and \( T \) is the temperature in Kelvin.
Step 3: Calculate the total number of moles of air \( n \) using the ideal gas law rearranged as \( n = \frac{PV}{RT} \). Substitute the values for \( P \), \( V \), \( R \), and \( T \) into the equation.
Step 4: Determine the number of moles of oxygen by multiplying the total moles of air by the fraction of oxygen in the air (20%, or 0.20). \( n_{\text{oxygen}} = n \times 0.20 \).
Step 5: Convert the moles of oxygen to the number of oxygen molecules using Avogadro's number \( 6.022 \times 10^{23} \, \text{molecules/mol} \). Multiply \( n_{\text{oxygen}} \) by Avogadro's number to find the total number of oxygen molecules in the lungs.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
7mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Total Lung Capacity
Total lung capacity (TLC) is the maximum amount of air the lungs can hold, typically around 5.0 liters for an adult. It includes various lung volumes such as tidal volume, inspiratory reserve volume, and expiratory reserve volume. Understanding TLC is essential for calculating the amount of specific gases, like oxygen, present in the lungs after inhalation.
Recommended video:
Guided course
05:29
Total Internal Reflection
Gas Composition and Molar Volume
The composition of air at sea level is approximately 78% nitrogen, 21% oxygen, and 1% other gases. The molar volume of an ideal gas at standard temperature and pressure (STP) is about 22.4 liters per mole. This concept is crucial for determining the number of moles of oxygen in the lungs based on the total lung capacity and the percentage of oxygen in the air.
Recommended video:
Guided course
07:47Vector Composition & Decomposition
Avogadro's Number
Avogadro's number, approximately 6.022 x 10²³, is the number of molecules in one mole of a substance. This constant allows us to convert moles of a gas into the actual number of molecules. In the context of the question, it is used to find the total number of oxygen molecules present in the lungs after inhalation by multiplying the moles of oxygen by Avogadro's number.
Recommended video:
Guided course
07:19Moles & Avogadro's Number
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?
1
views
Textbook Question
A gas at 100°C fills volume V0. If the pressure is held constant, what is the volume if the Celsius temperature is doubled?
1
views
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?
1
views
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?
1
views
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.
2
views