Using Gibbs Free Energy

  • thermodynamics entropy heat capacity internal energy equation of state
  • Energy and Entropy 2020

    You are given the following Gibbs free energy: \begin{equation*} G=-k T N \ln \left(\frac{a T^{5 / 2}}{p}\right) \end{equation*} where \(a\) is a constant (whose dimensions make the argument of the logarithm dimensionless).

    1. Compute the entropy.

    2. Work out the heat capacity at constant pressure \(C_p\).

    3. Find the connection among \(V\), \(p\), \(N\), and \(T\), which is called the equation of state (Hint: find the volume as a partial derivative of the Gibbs free energy).

    4. Compute the internal energy \(U\).