A bubble has surface tension S . The ideal gas inside the bubble has ratio of specific heats γ = 5 3 . The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is P a 1 , the radius of the bubble is found to be r 1 and the temperature of the enclosed gas is T 1 . When the atmospheric pressure is P a 2 , the radius of the bubble and the temperature of the en

Step-by-step solution

When, Pressure Radius Temperature P a 1 → r 1 → T 1 P a 2 → r 2 → T 2 For adiabatic process P 1 V 1 γ = P 2 V 2 γ P a 1 + 4 T r 1 4 3 π r 1 3 5 3 = P a 2 + 4 T r 2 4 3 π r 2 3 5 3 r 1 r 2 5 = P a 2 + 4 T r 2 P a 1 + 4 T r 1 Therefore, option A is incorrect. Now, T 1 V 1 γ - 1 = T 2 V 2 γ - 1 T 2 T 1 = V 1 V 2 γ - 1 = r 1 r 2 3 2 3 T 2 T 1 = P a 2 + 4 T r 2 P a 1 + 4 T r 1 2 5 Therefore, option D is correct. For option B Total internal energy + surface energ