JEE Advanced 2022 Physics question

A bubble has surface tension . The ideal gas inside the bubble has ratio of specific heats . The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is , the radius of the bubble is found to be and the temperature of the enclosed gas is . When the atmospheric pressure is , the radius of the bubble and the temperature of the enclosed gas are and , respectively. Which of the following statement(s) is(are) correct?

• (A)If the surface of the bubble is a perfect heat insulator, then .
• (B)If the surface of the bubble is a perfect heat insulator, then the total internal energy of the bubble including its 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 negligible, then .Correct
• (D)If the surface of the bubble is a perfect heat insulator, then .Correct