JEE Advanced2024PhysicsMechanical Properties of FluidsActual
A spherical soap bubble inside an air chamber at pressure P₀=10^5 ~Pa has a certain radius so that the excess pressure inside the bubble is P=144 ~Pa . Now, the chamber pressure is reduced to 8 P₀ / 27 so that the bubble radius and its excess pressure change. In this process, all the temperatures remain unchanged. Assume air to be an ideal gas and the excess pressure P in both the cases to be much smaller than the ch
Correct answer
0
Step-by-step solution
Case-1 aligned & P - P ₀= P = 4 ~T R & P = ( P ₀+ 4 ~T R ) aligned Case-2 aligned & P ₁- 8 P ₀ 27 = P ₁= 4 ~T R ₁ & P ₁= 4 ~T R ₁ + 8 P ₀ 27 aligned Constant temperature process aligned & PV = P ₁ ~V ₁ & ( P ₀+ 4 ~T R ) 4 3 R ^3= ( 4 ~T R ₁ + 8 P ₀ 27 ) 4 3 R ₁^3 ; ( 4 ~T R ), ( 4 ~T R ₁ ) (Neglected) & R = 2 3 R ₁ R ₁= 3 2 R & P ₁= 4 ~T R ₁ = 4 ~T 3 R 2= 2 3 (144)=96 ~Pa aligned