Question

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 $\left(4 \pi p_{0} R a^{2}\right) X$, where $X$ is a constant and $\gamma=\frac{C_{ p } }{ C_{ V }}=\frac{41 }{ 30}$. The value of $X$ is ______

Answer 1

The value of X is 2.05