Statistical Mechanics Calculator
Compute partition function, entropy, and average energy for two-state systems and ideal gases with detailed step-by-step solutions and thermodynamic insights.
Formulas Used
- β = 1 / (kT)
- Partition Function: Z = Σ e^(-βEᵢ)
- Entropy: S = k ln Ω
- Multiplicity: Ω = N! / (N₁! (N − N₁)!)
- Average Energy: ⟨E⟩ = Σ (Eᵢ e^(-βEᵢ)) / Z
- Ideal Gas:
- Thermal wavelength: λ = √(h² / (2π m k T))
- Partition Function: Z = V / λ³
- Entropy: S = N k [ln(V / (Nλ³)) + 5/2]
- Average Energy: ⟨E⟩ = (3/2) kT
Partition Function Details
- - Measures number of accessible microstates in a system.
- - Higher Z means more thermodynamic probability.
- - Strongly depends on temperature and energy levels.
- - Foundation of all thermodynamic properties.
- Two-State System Notes:
- - System has only two energy levels (E₁, E₂).
- - Useful for quantum and spin systems.
- - Probability follows Boltzmann distribution.
- - Simple model for understanding statistical mechanics.