An igniter is needed for a rocket motor similar to one shown in Fig. 12-1. Igniters have been designed by various oversimplified design rules such as Fig. 14-3. The motor has an initial internal grain cavity volume of 0.055 m³ and an initial burning surface of 0.72 m². The proposed igniter propellant has these characteristics: combustion temperature 2500 K and an energy release of about 40 J/kg-sec. Calculate the minimum required igniter propellant mass

(a) if the cavity has to be pressurized to about 2 atm (ignore heat losses);

(b) if only 6% of the igniter gas energy is absorbed at the burning surface, and it requires about 20 cal/cm²-sec to ignite in about 0.13 sec.