1.4 Second Axiom of Thermodynamics: Irreversible Processes exist

• A System never changes by its own into a less probable state

• There exists no perpetuum mobile of second kind

• \begin{equation*} \delta Q / T \lt = dS \qquad \delta Q_{rev} / T = dS \qquad S: \mbox{Entropy} \end{equation*}

  (1.4)

  Into first axiom:

  \begin{equation*} dU = T dS - dW \end{equation*}

  (1.5)

• \(S\) is a state variable

• \(U\) is a potential \(U(S,...)\) for reversible processes

• \(dU\) is a total differential

• \(S\) increases until thermodynamic equilibrium is reached and afterwards it always has its maximal value; thermodynamic potentials only apply for equilibrium

This knowledge opened the way to heat transforming machines \(\Rightarrow\) optimization of the efficiency
Thermodynamic is a ”perfect mathematical game”: Based on a minimal set of axioms many results are concluded (many different relations contain the same physical information)

© J. Carstensen (Stat. Meth.)