Skip to ContentGo to accessibility page
OpenStax Logo
University Physics Volume 2

Summary

University Physics Volume 2Summary

Summary

2.1 Molecular Model of an Ideal Gas

  • The ideal gas law relates the pressure and volume of a gas to the number of gas molecules and the temperature of the gas.
  • A mole of any substance has a number of molecules equal to the number of atoms in a 12-g sample of carbon-12. The number of molecules in a mole is called Avogadro’s number NA,NA,
    NA=6.02×1023mol−1.NA=6.02×1023mol−1.
  • A mole of any substance has a mass in grams numerically equal to its molecular mass in unified mass units, which can be determined from the periodic table of elements. The ideal gas law can also be written and solved in terms of the number of moles of gas:
    pV=nRT,pV=nRT,
    where n is the number of moles and R is the universal gas constant,
    R=8.31J/mol·K.R=8.31J/mol·K.
  • The ideal gas law is generally valid at temperatures well above the boiling temperature.
  • The van der Waals equation of state for gases is valid closer to the boiling point than the ideal gas law.
  • Above the critical temperature and pressure for a given substance, the liquid phase does not exist, and the sample is “supercritical.”

2.2 Pressure, Temperature, and RMS Speed

  • Kinetic theory is the atomic description of gases as well as liquids and solids. It models the properties of matter in terms of continuous random motion of molecules.
  • The ideal gas law can be expressed in terms of the mass of the gas’s molecules and v2–,v2–, the average of the molecular speed squared, instead of the temperature.
  • The temperature of gases is proportional to the average translational kinetic energy of molecules. Hence, the typical speed of gas molecules vrmsvrms is proportional to the square root of the temperature and inversely proportional to the square root of the molecular mass.
  • In a mixture of gases, each gas exerts a pressure equal to the total pressure times the fraction of the mixture that the gas makes up.
  • The mean free path (the average distance between collisions) and the mean free time of gas molecules are proportional to the temperature and inversely proportional to the molar density and the molecules’ cross-sectional area.

2.3 Heat Capacity and Equipartition of Energy

  • Every degree of freedom of an ideal gas contributes 12kBT12kBT per atom or molecule to its changes in internal energy.
  • Every degree of freedom contributes 12R12R to its molar heat capacity at constant volume CV.CV.
  • Degrees of freedom do not contribute if the temperature is too low to excite the minimum energy of the degree of freedom as given by quantum mechanics. Therefore, at ordinary temperatures, d=3d=3 for monatomic gases, d=5d=5 for diatomic gases, and d≈6d≈6 for polyatomic gases.

2.4 Distribution of Molecular Speeds

  • The motion of individual molecules in a gas is random in magnitude and direction. However, a gas of many molecules has a predictable distribution of molecular speeds, known as the Maxwell-Boltzmann distribution.
  • The average and most probable velocities of molecules having the Maxwell-Boltzmann speed distribution, as well as the rms velocity, can be calculated from the temperature and molecular mass.
PreviousNext
Order a print copy
Citation/Attribution
Reuse and redistribution of this content in digital or print format:
  • This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's prior written permission.
  • This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License, which means that you can reuse and modify the material only for noncommercial purposes, must attribute OpenStax, and must distribute any derivative works under the same license.
  • Any commercial printing of this textbook, including using a local or custom printer, must be approved by OpenStax, and proper citation provided.
  • OpenStax-copyrighted images, activities, assessments, and similar components of this book are subject to the same licensing – CC-BY-NC-SA. They can be used for noncommercial purposes with attribution. Commercial use requires permission.
  • Permission requests: Anyone who intends to incorporate this content (including text, images, and other components) into large language models, use it in AI offerings, use it commercially (including in print), and/or has questions about another use case is welcome to complete our reuse request form.
Attribution information
  • If you are redistributing all or part of this book in a noncommercial print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/university-physics-volume-2/pages/1-introduction

  • If you are redistributing all or part of this book in a noncommercial digital format, then for every page that includes OpenStax content, you must license the derivative work under the same CC-BY-NC-SA license as the original, and include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/university-physics-volume-2/pages/1-introduction

Citation information

The information below includes the information needed to generate citations in most major styles (APA, MLA, etc.); you must reformat and organize the information as needed to fit the requirements of the style. Use the information below to generate a citation. We recommend using a citation tool such as this one.

© Jun 11, 2026 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo, and Rice University name, and Rice University logo trademarks, or wordmarks are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.