Question

4. A spherical balloon of 0.5 m diameter contains air at a pressure of 500 kPa. The diameter increases to 0.55m in a reversible process during which pressure is proportional to diameter. Determine the work done by the air in the balloon during this process. Also calculate the final pressure.

Answer 1

From the condition of the process P = CD

Where p is the pressure (kPa)

C is a constant

D is the diameter (m) From the initial condition

500 = C * 0.5

C = 500 / 0.5 = 1000 Therefore

P = 1000 D

₁W₂ =$\int$ 1000DdV

To substitute dV in terms of dD Consider the volume of the sphere

$V=\pi /6 (D)$ ³

Now,

$=500*\pi/4$ (0.55⁴-0.50⁴)

$=11.39 KJ$

Final pressure

P2 = 100

D2 = 1000 * 0.55

= 550 kPa