JEE Advanced2020PhysicsThermodynamicsActual
A spherical bubble inside water has radius R . Take the pressure inside the bubble and the water pressure to be p 0 . The bubble now gets compressed radially in an adiabatic manner so that its radius becomes ( R - a ) . For a ≪ R the magnitude of the work done in the process is given by 4 π P 0 R a 2 X , where X is a constant and γ = C p / C V = 41 / 30 . The value of X is______
Correct answer
0
Step-by-step solution
( aligned & W =( P )_ avg 4 R ^2 a &= | dP 2 4 R ^2 a | aligned ) (for small change (( P )_ avg ) arithmetic mean) (= PV gamma = c dP =- P V dV =- P ₀ ~V 4 R ^2 a ) (= P ₀ 2 ~V 4 R ^2 a 4 R ^2 a ) (= P ₀ 2 4 R ^3 4 R ^2 a 4 R ^2 a ) (= (4 pRP a ^2 ) 3 2 ) ( x =2.05 )