Boltzmann's Constant and Ludwig Boltzmann

Ludwig Boltzmann

• Lived in the late 1800s and early 1900s.
• Father of modern atomic theory: Advocated that matter is made of atoms and molecules.
  • This was not an obvious concept 120 years ago.
• Atomic theory explanation:
  • Example: Gas (like steam) in a container is made up of atoms/molecules.
  • Heat energy is kinetic energy of molecules (e.g., H2O molecules in steam).
  • High temperature indicates large average kinetic energy of gas molecules.

Kinetic Molecular Explanation

• Heat energy isn't new; it's kinetic energy of particles.
• Fast-moving molecules transfer kinetic energy to objects (e.g., your hand in steam).
• Temperature relates to the average kinetic energy of molecules.

Ideal Gas Law

• Formula: PV = nRT
  • P = Pressure (pascals)
  • V = Volume (meters cubed)
  • n = Number of moles
  • R = Gas constant (8.31 J/mol K)
  • T = Temperature (Kelvin)

Boltzmann's Constant

• Transition from the macroscopic view of gases to microscopic:
  • Ideal gas law can be written as PV = NkT
  • N = Number of molecules (instead of moles).
  • k (Boltzmann's constant) needed due to large N.
  • Value of Boltzmann's Constant:
    • k = 1.38 × 10^-23 J/K
  • Calculated as (1/Avogadro’s number) × R.
  • R = 8.31 J/mol K, Avogadro’s number = 6.02 × 10^23.

Importance of Boltzmann's Constant

• Allows writing of microscopically focused ideal gas law.
• Fundamental in statistical and thermal mechanics.
• Inscribed on Boltzmann's gravestone as part of the equation for entropy:
  • S = k ln(W)
  • S = Entropy
  • W = Number of microstates

Entropy

• Entropy relates to disorder and available energy in a system.
• Equation: S = k ln(W) (uses natural logarithm).
• W is the number of microstates that result in the same macroscopic appearance.
• Entropy is a complex, fascinating concept that merits further exploration.