Adiabatic Fire Starter

A plan for an adiabatic fire starter is shown above. (This is the sort of thing bored physicists design in their spare time.) It consists of an adiabatic cylinder fitted with a frictionless, insulated piston. Tinder placed in the bottom of the cylinder that will ignite if the air around it ever gets above 900 $^\circ$K. If one whacks the piston shaft hard with a sledgehammer the piston does work on the gas as it compresses it. If one hits hard enough, you pull out the piston, shake out the tinder, blow on it and voila! A hard-earned flame!

a) Assuming that the air in the cylinder is an ideal diatomic gas and that it starts with $P_i = 1$ atm $\approx 10^5$ N/m$^2$, $V_i = 0.01$ liter (10 cm$^3$), and $T_i = 300 ^\circ$ K, what is its heat capacity at constant volume, $C_v$? At constant pressure, $C_p$? How many molecules of air are there in the cylinder?

b) Find the approximate amount of initial (kinetic) energy that must be imparted to the piston by the sledgehammer in order to ignite the tinder. Is it reasonable to expect to get this much energy from a 2.5 kg sledgehammer operated by muscle power?