BB guns are typically air rifles employing compressed air in a small (1 cm3) cyl
ID: 1348086 • Letter: B
Question
BB guns are typically air rifles employing compressed air in a small (1 cm3) cylinder to propel a projectile. The typical pressure inside the cylinder when the gun is ready to fire is around 1 MPa. The BBs have a mass of 15 g, and they act as the piston head as they are held by a pin (attached to the trigger). When the trigger is pulled, the pin is released and the air expands in an isothermal process (T = constant). If the air pressure is 0.1 MPa in the cylinder as the BB exits, find
a. The final volume and the mass of air.
b. The work done by the air as it expands and work done on the atmosphere.
c. The work imparted to the bullet and the bullet exit velocity.
Energy Balances —using ideal gas law relationships
Explanation / Answer
P1 = 1 Mpa
P2 = 0.1MPa
V1 = 1 cm^3
V2 = ?
in isothermal process
P1*V1 = P2*V2
V2 = (P1*V1)/P2
V2 = (1*1)/0.1 = 10 cm^3
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part(b)
W = 2.303*P1*V1*log(P1/P2)
W = 2.303*10^6*1*10^-6*log(1/0.1)
W = 2.303 J
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from work energy
work done = change in KE
2.303 = 0.5*m*(vf^2-vi^2)
vi = initial speed = 0
2.303 = 0.5*0.015*v^2
v = 17.52 m/s <<-----answer
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