An explosion creates a spherically shockwave propagating radially into still air at p1=101 kPa and T1=293 K. A recording instrument registers a maximum pressure of p2=506 kPa as the shock wavefront passes by. The adiabatic coefficient of air for this compression shock is γ=1.4, the molar mass of air is M=29.0 g/mol and the ideal gas constant is R=8.314 J/(mol⋅K).
C2.1 Determine the air temperature increase under the action of the compression shock.
C2.2 Determine the Mach's number corresponding to the speed of the shockwave.
C2.3 Determine the wind's speed following the shock wavefront, with respect to a fixed observer.
C2.4 During the compression shock the gas temperature and pressure sharply increase, much more than in a quasistatic adiabatic compression. After the shock, the gas expands adiabatically, but because the slope of the adiabatic process is smaller than that of the adiabatic shock, when the gas density reaches again the initial value, its pressure is still higher than that of the unperturbed gas, p1. Derive the ratios p1p3 and T1T3 at the end of the expansion process and calculate the numerical values of p3 and T3.
C2.5 From this point the gas is cooling until it reaches the initial state. Assuming that for the entire cyclic process the adiabatic exponent has the same value, derive an expression for the entropy variation of the mass unit of air during the compression shock and calculate its numerical value.