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 pr

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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 &#8810; R the magnitude of the work done in the process is given by 4 &#960; P 0 R a 2 X , where  X is a constant and  &#947; = C p / C V = 41 / 30 . The value of  X is______

Quantrex Academy · Accepted Answer

Correct answer: A. A

$ 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$

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