Answers
The kinetic energy of bullet is
E = 1/2 * m * v2
E = 1/2 * 1e-3 * 1002
E = 5 J
Therefore, work done on the gas is -5 J
Now, use equations for adiabatic expansion
W = (1 / - 1) ( PfVf - Pi Vi) --------------- (1)
Here,
Vf = 15 cm3 + 0.015 * 40
Vf = 15.6 cm3
= 1.4 (diatomic gas)
so,
Also
Pf = Pi (Vi / Vf)
Put this is (1) and solve for initial pressure , Pi
Pi = 8.565e6 Pa