Question

An air bubble of volume V is released from the bottom of a lake which has a depth of 11 m. Find the volume of the bubble at the surface of the lake. The water has density $1000kg/m^3$. At the release point of the bubble and at the surface, temperature is $4^{\circ }C$. The atmospheric pressure is $1.01\times {10}^{5}N/m^2$.

• A. $12.089V$
  
• B. $7.089V$
• C. $2.089V$
• D. $8.089V$

Answer 1

The correct option is C $2.089V$

Given : $P_1=1.01\times {10}^5$ $N/m^2$ $V_2=V$ $h=11$ m $\rho =1000$ $kg/m^3$

Pressure at a depth h $P_2=P_1+\rho gh$

$\therefore$ $P_2=1.01\times {10}^5+1000\left(10\right)\left(11\right)=2.11\times {10}^5$ $N/m^2$

Using $P_1{V}_1=P_2{V}_2$

$\therefore$ $1.01\times {10}^5\times V_1=$ $2.11\times {10}^5\times V$ $⟹V_1=2.089V$