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 5 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~room temperature). 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

Answer 1

Sed initial Pressure Pi= Impe Initial volume Vi= 1 cm² 15 m² Find Pressure = 0 MP.. Let VF be Find volume T= Room temp=20°C=2964 Constat for isothermal expension of Gos Pu=Constat. i Pi V; = PP VE Ve=1 X 2 Tocm3 l @ 01 Man RT 8.31472883 Now, ui t n = pv = 4x10x10 6 4-03 1157 malena immessa 4.03 x16x22510-0117g) a MM4,239 Find most of Ara PE VEXM.M=0-1x 10 xloxio x29 to 01175! RT 8314x298

(6) nork done during iso themd Process WART Ln( VF - 8.31442992 In{1p) = 5704-9234 W = 5704.42 x 10 x 4.033.999 Il Work done on Atmosphere against constant po wz petu (vş - Vi)= 165(10-11416"=10093. (6) hork imperted to bullet - Ne-N7= 2.89-0-9 -1399 I. ; Chonge in Kinetic energy work done (A pe work eney :: 1399= my • VE 1-39742 = 55.9 N=748 m/ Sx?

using isothermal conditiona and ideal gas law along with work energy theroem we can find the required variables.

for any doubts please write in comments.