Entropy

Thermodynamics

$\Delta S=\frac{Q_{\text{reversible}}}{T}$

• $\Delta S$ is the change in entropy of the system
• $Q_{\text{reversible}}$ is the heat gained or loss by the system in a reversible process
• $T$ is the temperature of the system

$\Delta S_{\text{universe}}=\Delta S_{\text{system}}+\Delta S_{\text{surroundings}}$

$\Delta S=nR\ln \left(\frac{V_f}{V_0}\right)$

• Entropy change in free expansion going from volume $V_0$ to $V_f$
• Derivable by Sackur–Tetrode Equation

Statistical Mechanics

Topics

• Sackur–Tetrode Equation
• Gibb’s Entropy

$S=k_B\ln \Omega$

• The statistical mechanics definition of entropy
• $k_B$ is the [Boltzmann Constant]
• $\Omega$ is multiplicity of the system
• Sackur–Tetrode Equation

Entropic Time