Questions

• What makes reservoirs a special kind of phase?
• Give an expression for the infinitesimal $\textrm{d}H$, where $H$ is the enthalpy.
• What are the values of the following partial derivatives: $\left( \frac{\partial H}{\partial P} \right)_S$ and $\left( \frac{\partial H}{\partial S} \right)_P$
• Give an expression for the infinitesimal $\textrm{d}F$, where $F$ is the Helmholtz free energy.
• What are the values of the following partial derivatives: $\left( \frac{\partial F}{\partial V} \right)_T$ and $\left( \frac{\partial F}{\partial T} \right)_V$
• Gibbs free energy The Gibbs free energy is defined as $G = H - TS$, where $H$ is the entropy. Use what you have learnt from the video to find an expression for the infinitesimal $\textrm{d}G$ and the values of $\left( \frac{\partial G}{\partial P} \right)_T$ and $\left( \frac{\partial G}{\partial T} \right)_P$
• Grand potential The Grand potential is defined as $\Omega = E - TS - \sum_i \mu_i n_i$. Use what you have learnt from the video to find an expression for the infinitesimal $\textrm{d}G$. You will need to use an extended form of the first and second laws of thermodynamics: $\textrm{d}E = T\textrm{d}S - P\textrm{d}V + \sum_i \mu_i \textrm{d}n_i$. Use the expression you derived to find values for $\left( \frac{\partial \Omega}{\partial V} \right)$, $\left( \frac{\partial \Omega}{\partial T} \right)$ and $\left( \frac{\partial \Omega}{\partial \mu_i} \right)$