The piston diameter is Dp = 3 mm and the piston position is initially s1 = 5 cm from the bottom of the piston. At this point, the balloon diameter is Db,1 = 3.5 mm and the pressure and temperature of the helium in the piston and the balloon are P1 = 103 kPa and T1 = 22°C, respectively. The balloon stretches as it is filled and so the pressure in the balloon increases. The relationship between the pressure within the balloon and the volume of the balloon is given by:
P = Patm + KbVb
where Patm is atmospheric pressure (1 atm) and Kb is a constant. The piston is pushed downwards causing the balloon to fill. The final diameter of the balloon is Db,2 = 7 mm.
Assume that the piston and balloon are both leak-tight. You may ignore the volume of the tube connecting the balloon to the piston. The pressure in the piston and the pressure in the balloon are always the same. What is the work transfer from the helium to the balloon during the filling process (J)?