Consider a shock wave moving through air at $293$ K and $1$ atm. Immediately downstream $($behind$)$ the shock wave, the air temperature and pressure increase to $790$ K and $9\mathrm{.}656$ atm. Calculate the changes in the following quantities across the wave $($show details of your calculation$)$:

a$.$ Enthalpy

b$.$ Internal energy

c$.$ Entropy