Free energy of a two state system

  • Helmholtz free energy entropy statistical mechanics
  • Thermal and Statistical Physics 2020
    1. Find an expression for the free energy as a function of \(T\) of a system with two states, one at energy 0 and one at energy \(\varepsilon\).

    2. From the free energy, find expressions for the internal energy \(U\) and entropy \(S\) of the system.

    3. Plot the entropy versus \(T\). Explain its asymptotic behavior as the temperature becomes high.

    4. Plot the \(S(T)\) versus \(U(T)\). Explain the maximum value of the energy \(U\).