Consider a blunt-nosed aerodynamic model mounted inside the driven section of a shock tube. The axis of the model is aligned parallel to the axis of the shock tube, and the nose of the model faces toward the oncoming incident shock wave. The driven gas is air initially at a temperature and pressure of \(300 \mathrm{~K}\) and \(0.1 \mathrm{~atm}\), respectively. After the diaphragm is broken, an incident shock wave with a pressure ratio of \(p_{2} / p_{1}=40.4\) propagates into the driven section.

a. Calculate the pressure and temperature at the nose of the model shortly after the incident shock sweeps by the model.

b. Calculate the pressure and temperature at the nose of the model after the reflected shock sweeps by the model.