Lecture Notes: Kinetic Theory and Gas Dynamics

Average Kinetic Energy and Temperature

• Relating Average Kinetic Energy to Temperature
  • Understanding how kinetic energy and temperature are correlated.

Root Mean Squared Velocity (RMS Velocity)

• Definition and Calculation

  • RMS Velocity: sqrt(3 * k_B * T / m)
    • k_B: Boltzmann constant
    • T: Temperature
    • m: Mass of the gas molecule
  • As temperature increases, velocity increases as square root of temperature.
  • More massive molecules move slower for the same kinetic energy.

• Real-World Application

  • Average velocity of room temperature nitrogen: 500 m/s.

Air Resistance in Physics Labs

• Why Air Resistance is Negligible
  • Average speed of gas molecules (500 m/s) vs. typical speeds (1 m/s) in physics labs.
  • Gas molecules easily move out of the way at low speeds.

Maxwell-Boltzmann Distribution

• Characteristics
  • Speed distribution of gas molecules.
  • Higher temperatures stretch the distribution curve.

Helium and Hydrogen in the Atmosphere

• National Helium Shortage

  • Helium used in balloons reduces availability for scientific labs.

• Escape Velocity and Atmospheric Composition

  • Light gases like hydrogen and helium can escape Earth’s gravitational field.
  • Helium and hydrogen constantly being lost to space.
  • Source of Hydrogen: Water dissociation by lightning.
  • Source of Helium: Radioactive decay in rocks.

• Sound Changes with Different Gases

  • Helium changes speed of sound, affecting resonance and pitch of voice.
  • Sulfur hexafluoride: heavier gas, lowers voice dramatically.