A bubble has surface tension S . The ideal gas inside the bubble has ratio of specific heats $\gamma=\frac{5}{3}$. The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is $\mathrm{Par}_1$, the radius of the bubble is found to be $\mathrm{r}_1$ and the temperature of the enclosed gas is $\mathrm{T}_1$. When the atmospheric pressure is $\mathrm{Pa}_2$, the radius of the bubble and the temperature of the enclosed gas are $\mathrm{r}_2$ and $\mathrm{T}_2$, respectively. Which of the following statement(s) is(are) correct?
Select ALL correct options:
A
If the surface of the bubble is a perfect heat insulator, then $\left(\frac{r_1}{r_2}\right)^5=\frac{P_{a 2}+\frac{2 S}{r_2}}{P_{a 1}+\frac{2 S}{r_1}}$
B
If the surface of the bubble is a perfect heat insulator, then the total internal energy of the bubble including surface energy does not change with the external atmospheric pressure.
C
If the surface of the bubble is a perfect heat conductor and the change in atmospheric temperature is hegligible, then $\left(\frac{r_1}{r_2}\right)^3=\frac{P_{a 2}+\frac{4 S}{r_2}}{P_{a 1}+\frac{4 S}{r_1}}$
D
If the surface of the bubble is a perfect heat insulator, then $\left(\frac{T_2}{T_1}\right)^{\frac{5}{2}}=\frac{P_{a 2}+\frac{4 S}{r_2}}{P_{a 1}+\frac{4 S}{r_1}}$
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