Pressure varies linearly with diameter
That means P α D
Or, P/D = constant
At 1 bar (105 Pa), Diameter, D = 0.5m
Thus the constant is 105
/0.5 = 2 × 105
Using the value of this constant, we can calculate the value of final diameter when P = 4 × 105
. Thus
we have initial and final diameter.
Now,
Work done =
∫ P. dV
Vfinal
Vinitial
= ∫ (2 × 105D). d (
Π
6
D
3) =
Dfinal
Dinitial
∫ (2 × 105D).
Π
6
3D
2 d(D
3)