A spherical balloon contains air at temperature To and pressure Po. The balloon material is such that the instantaneous pressure inside is proportional to the square of the diameter. when the volume of the balloon doubles as a result of heat transfer, the expansion follows the law :

PV^-2/3 = constant

Pressure is directly proportional to square of the diameter of the balloon.

\(\frac{P_2}{P_1} = \frac{D^2_2}{D^2_1}\) ... (i)

As : \(V_2 = 2 V_1 \Rightarrow D^3_2 = 2D^3_1\) 

\(\frac{D_2}{D_1} = (\frac{V_2}{V_1})^{1/3}\) ... (ii)

From eq : (i) and (ii) - 

\(\Rightarrow \frac{P_2}{P_1} = (\frac{V_2}{V_1})^{2/3}\)

Thus, \(PV^{-2/3} = constant\)