6: Properties of Gases
- Page ID
- 7248
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 6.1: The Ideal Gas Equation
- This page discusses Robert Boyle's experiments from 1660 that led to Boyle's Law, which states that pressure is inversely proportional to volume for a fixed mass of gas at constant temperature. It also covers the relationship between gas volume and temperature at constant pressure, and the relationship between pressure and temperature at constant volume.
- 6.2: Real Gases
- This page discusses the behavior of real gases in relation to the ideal gas equation, emphasizing their conformity under high temperatures beyond the critical point. It explains the compression factor (Z) and its significance in measuring deviations from ideal gas behavior with respect to pressure.
- 6.3: Van der Waals and Other Gases
- This page explores the behavior of real gases and their approximation to ideal gases under specific conditions. It highlights various equations of state, notably van der Waals', which considers molecular interactions and helps understand gas behavior near critical points. Critical constants are essential for identifying gas properties, while the virial equation provides another perspective using coefficients.
- 6.4: Gas, Vapour, Liquid and Solid
- This page explores the behavior of substances during phase transitions, focusing on critical points in PV and PT planes. It defines phases of matter—solid, liquid, gas—and highlights water's unique expansion upon freezing. The discussion includes the transition to supercritical fluids and the ambiguity in classifying materials like glass. It emphasizes the influence of temperature and pressure on boiling points, vapor pressures, and density changes.
- 6.5: Kinetic Theory of Gases- Pressure
- This page examines the connection between the microscopic properties of ideal gases, highlighting how pressure, temperature, and molecular density relate to molecular speed. It explains momentum changes during wall collisions to derive the pressure equation \( P=\frac{1}{3} n m \overline{c^{2}} \), linking pressure to speed and density.
- 6.6: Collisions
- This page examines key concepts of molecular collisions in gases, detailing mean time between collisions, mean free path, and collision rates. It utilizes a hard sphere model and collision cross-section area for calculations. The section also covers average relative speeds, adjusts collision metrics accordingly, and discusses the complexities of the Maxwell-Boltzmann speed distribution.
- 6.7: Distribution of Speeds
- This page covers the velocity distribution of gas molecules, focusing on the Gaussian distribution for velocity components and deriving the Maxwell-Boltzmann distribution for speeds. It emphasizes the symmetry of the distribution, uses even powers of velocity components, and explains the relationship of molecule fractions to the Gaussian function. Key constants and integrals define mean, RMS, and median speeds, concluding with their implications in thermodynamics.
- 6.8: Forces Between Molecules
- This page explores intermolecular forces, focusing on van der Waals and Coulomb forces and their impact on gas behavior as described by Boyle's Law. It introduces the Lennard-Jones potential for van der Waals interactions and the Morse potential for bound molecular forces. Additionally, the page discusses the mathematical properties of these potentials and their importance in deriving the equation of state.
Thumbnail: In an ordinary gas, so many molecules move so fast that they collide billions of times every second. (Public Domain; Greg L via Wikipedia)