An air bubble of volume V_o is released by a fish at a depth h in a lake. The bubble rises to the surface. Assume constant temperature and standard atmospheric pressure P above the lake. The volume of the bubble just before touching the surface will be (density of water is \(\rho\)) :

\(V_o[1 + \frac{\rho g h}{P}]\)

According to Boyle's law, since temperature is constant hence product of pressure and volume will remain constant at the bottom and the top :

If P is the atmospheric pressure at the top of the lake and the volume of bubble is V then from P₁V₁ = P₂V₂

$ (P_a + h \rho g)V_0= P_a V$

\(\Rightarrow V = \frac{P_a + h \rho g}{P_a} V_o\)

V = \(V_o[1 + \frac{\rho g h}{P_a}]\)